Knowledge talk:WikiProject Mathematics/Archive/2017/Nov

3485:

the beginning of that very long discussion 'However, note a difference: on my courses I am the decision maker; here on Knowledge I am not. Here a point of view cannot be presented until/unless it is widely used. And if it is, it must be presented with "due weight"'. Practically everything else there was irrelevant to improving the article which is the purpose of a talk page. The appropriate answer to him when he quoted Bourbaki and said though a definition was formally correct it was absurd is to say he needs a better source to say so than himself. No source was provided never mind a better one.

2790:". Again this is too restricted, as it is basically a concept in algebra that is used in various other areas of mathematics. Moreover, "flat module" may be encountered in various areas that have nothing to do with mathematics, and I am not sure that it is clear for every people interested in these areas that homological algebra and algebraic geometry are mathematics. Therefore, in these two cases, the best begin is "In mathematics", without link. There are a lot of similar examples. 5691:"Cauchy's description" is already in use in the following sense (explained by me on Hessel's talk page, but apparently not understood). Mathematics works with notions rather than definitions. A notion is, effectively, an equivalence class of definitions. There is no gain in canonizing one definition and exterminating all others. It is better to know many equivalent definitions, and to understand their interplay (which needs mathematical maturity, sometimes missing). See 3058:

discussion, a numerical series converges to pi need to be somehow distinguished from pi, even writing down pi itself involves some infinite expression. I don't think the language in mathematics that is currently in use is able to take these nuances into account. I guess one mathematically rigorous way is to somehow encode the construction that is used to obtain the results; i.e., histories behind objects. I'm sure the resulting approach to calculus should be called

2014: 40: 2026: 4863:.) So here the sums/series denote particular distributions. My larger point was that the insistence on a unique interpretation seems unworkable not only atypical. For instance, I don't think there is a clean bright distinction between sum and series. The right-hand side in the above example seems better to be called sum than series. Likewise, any infinite sum involving partition of unity feels like sum than series. -- 4070:.) Doesn't this fits with the (universal) practice: 'series' is used instead of 'sequence' in situations where it's essential that addition between terms is defined? And doesn't this fits with the contents of the chapters headed 'Sequences' and 'Series' in almost all textbooks on calculus? (Keep in mind that Cauchy used 'convergent' for 'converging partial sums' = 'summable', not for 'converging terms'.) 5969:

do so anyway, and by demonstrating in your writing the same problems that previously caused you to be locked out from writing on those specific articles, you are only making it more likely that others will agree with the sense of that discussion. So, while your writing about this is not yet officially prohibited, it looks like it soon will be, and you are only hurting your own cause by doing it. —

1754: 3291:

this is consistent", or "more clear", or "less context-dependent", or "simpler", "more logical" etc). Maybe he hopes to gradually exterminate the word "series" this way. Anyway, he grossly exaggerates importance of all that. He believes that this is not just a pedagogical problem, but a mathematical problem, that mathematics is inconsistent (God forbid) because of that, etc.

4492:

former denotes the limit of the sequence 0.9, 0.99, ... and so (trivially??) is 1. But one might resonantly argue the former should mean a "number" that is arbitrary close to 1 but is less than 1; namely, 1 - infinitesimal. This is a matter of what calculus we are using. In some edge cases, the interpretations need not be obvious: the typical example is the "series"

2655:

makes it appear. Sometimes it is the right way to start, but other times there are better approaches and there are even instances where it is inappropriate (Element (mathematics) being one case in my opinion). Could we have a discussion of a better set of guidelines to use in mathematics articles for the purpose of putting the topic into context? --

1558: 1569: 4537:. I think by that one typically means Cauchy's principal value of the series. But arguably the best approach is to study such a series in the context of distributional calculus. In other words, it is fallacy to assume there is one unique consistent approach to calculus; we search for it in vain (no?) -- 2866:" is that the lay reader's unfamiliarity with the field may lead to confusion. Once there was an article titled "schismatic temperament," which I assumed, based on the title, was about a topic in psychiatry or the like, and I had to read several sentences before I found out it was about musical scales. 5968:

The admin discussion is currently looking like a pretty strong consensus that you should not be writing about sequences and series anywhere on Knowledge. "Anywhere on Knowledge" includes here (there is nothing in that discussion about limiting its restrictions to article space only). By continuing to

4211:

Or, distinguish explicitely the different roles of the s-word in: series-expression, series-representation, series-expansion, and more? And mention that 'sequence' and 'series' are synonyms (though sometimes one variant is more usual) in: alternating se..., Fibonacci-se..., Fourier-se..., geometric

3057:

Just some comment from an outsider: this seems to be mainly of a terminology issue. Is 1+1 the same as 2? Numerically speaking, the answer is trivially (I suppose) yes while the former is a sum and the later isn't; so in that sense they are different. The case of series is similar; for the purpose of

1283:

were lower case, so I mainly did this for consistency. I'm about to run out, so I can't look in too much more detail right now, but I'll quickly note that Mathworld and the Springer EOM both use lower case (although EOM hyphenates it) (and we certainly don't have to do the same as them, but it seems

4223:

I cannot provide sources that support the qualification 'absurd'. Nor sources that comment on 'series' defined as a sequence - sum sequence pair. I can show circa 10 titles of calculus books with their exposition on 'series' based on this pair; so it seems to be important enough to be mentioned in

3290:

However, whenever I try to elucidate such truth, he always disagrees: "but this is not my point". I fail to understand his point. In practice I observe that he attacks, here and there, an occurrence of the word "series" and insists on reformulating the text in order to remove this occurrence ("since

3167:

I don’t know enough philosophy to say how my early comment is related to logic. But Tsirel is correct: I was probably thinking of an abstract data type and such. In mathematics, we often casually compare two objects of different types: strictly speaking, series and number are incomparable but then I

2750:

IMO starting by "In mathematics" is useful, as, for many mathematics article, the title does not indicate clearly that they are about mathematics, and this introducing phrase is thus useful. However, everybody can understand this introducing phrase, and there is no need to follow the link or to know

2654:

In a related issue (actually more of a pet peeve of mine), I am distressed by the number of our articles that start with "In ], ...". This formulaic approach, meant to put the topic of the article into context, seems to not be as useful for readers, due to its generality, as the frequency of its use

5482:

Cauchy's nomenclature is consistent (although the adjective 'summable' instead of his adjective 'convergent' - close to the verb 'to converge' for 'tend to a limit' - could have avoided quite a lot of misunderstanding). In the adapted text, the word 'series' pops up in the fourth sentence without

4883:

A sort of a corollary of the above is that a certain superfluous looseness between sum/series/infinite expression isn't because mathematicians are sloppy but because they are not completely distinct concepts. Trying to suggest there is a bright distinction is both a POV and misleading, I think (not

3484:

It is not up to Knowledge editors no matter how knowledgeable or intelligent to reformulate mathematics in a more sensible or consistent way than is in current textbooks. They say series, we should say series. I really don't think there is very much more to it than that. As you pointed out right at

2632:

which describes a simple game of following wikipedia links, under a mild set of conditions. The claim is that 97% of the time one ends up at the Philosophy article. It is clear that by following the rules one must either end up at a sink (an article with no appropriate outgoing links) or in a loop.

2104:

could use a once-over. It contains some odd phrasing with jumbled or missing words, such as "because it's the truth value at some point is defined by it's truth value." At the very least, one of those "it's" seems unnecessary/wrong, but this is not my area and I don't really understand the sense of

4087:

idea, Tsirel; my comment: "Gedanken sind frei, wer kann sie erraten...". Actually I'm quite convinced, and I wrote it several times, that a chapter "Series" (and a chapter "Cesàro summability" connected with Fourier-expansion especially) would be much easier to understand by using 'sequence',

2997:

It seems hard if not impossible to reason with him or explaining him how Knowledge should approach a (math) topic. This issue has spread now over 3 Wikipedias, after starting out on the Dutch Knowledge and being told off there, he moved to English Knowledge and after the topic ban there on to the

4226:

One more remark on this quite unusual definition: Cauchy’s "sequence with real numbers as terms" implies that the partial sums are defined. So "a sequence with additionable terms" is close to "a sequence with a sum sequence", and in this interpretation of Bourbaki there’s nothing 'absurd' left

4491:

Some response to all of the above: I think it is useful to remember calculus that is currently taught and is in use is not the only one and not even necessary an optimum one. An example: is 0.999... the same as 1? This is mainly of the language problem. The "standard" interpretation is that the

6201:

Came across this article again for the first time in a while. Current article gives the impression that it is part of the scientific enterprise in a meaningful way and almost entirely avoids the fact that it is mostly just a nicely formatted crank magnet. Perhaps it could use some attention.

4088:'summable' and 'absolutely summable' instead of 'series', 'convergent' and 'absolutely convergent' (avoiding ambiguities). On the other hand, the objective "prepare a student (and a WP-user) to reading existing math literature", is as important to me as it is to you. That’s beyond discussion. 3294:

Really, is it possible to reformulate everything (equivalently) in a "series-free" language? Yes, of course. Every mathematician can easily reformulate a statement accordingly. (And by the way, this is why consistency of mathematics is still safe.) Instead of a series one may use the sequence

2703:

may be such a nudge; a "self-fulfilling prophesy" that some see as a challenge. Perhaps including a section on the distorting effect of such patterns on the utility of WP might at least produce a balancing nudge: link patterns that tend to encourage editors to browse new articles rather than

5652:

No one of the five attempts (in WP articles 'Series', 'Convergent series', 'Sequence') to describe the mathematical notion called 'series', is supported by any mentioned reliable and clear source. So Cauchy's (reworded by Bourbaki, used in the EoM) should be considered. That is my goal. --

6092:

It may happen that you are ready to take this challenge, but your name is hidden behind your username and you do not want to disclose it. In this case, do not reply here (or reply anonymously), register on Wikiversity under your true name and edit there. Contact me there on

1924: 1759:

Obviously the reason for the deficiency of space between "2" and "cas" was the use of \mbox{} instead of \operatorname{}. But both before and after that edit, we see less than the usual amount of space before and after than plus and minus signs, as exemplified here:

2816:,..." clause. Sometimes this is the correct thing to do, but rarely is the link useful, so I agree that this is often a case of overlinking. At other times something narrower is called for, but this needs to be readily identified as a branch of mathematics (like 5703:(which is good, not bad). Five (and more) equivalent (not at all "contradictory") definitions of a series is also a good, not bad, situation. One of these is "Cauchy's description" (which is just a historical fact of no special importance nowadays, I think so). 4251:

For goodness' sake. You just posted over 6000 bytes, and I have no idea what your point is, or if you even have one anymore. You've been overwhelming these discussions with walls of text, and it's not productive. Here's all you need to know: an (infinite)

2704:

previously seen articles would result in readers becoming aware of far more material. A mention of the disservice editors do when they amplify the observed effect might also help. On the "In mathematics" issue, I agree: that is what categories are for. —

2037:

MathML makes appropriate spaces around plus and minus better, PNG does not. And MathML creates much nicer glyphs for letters. Anyway I keep PNG rendering in my preferences, because MathML can sometimes fail to render horizontal lines, e.g. in fractions. :(

5749:

But (1): How can you write "Five (and more) equivalent .... definitions of a series is also a good ... situation." ? For that seems to say just the opposite of your "We do not have a single, universally accepted (and rigorous, of course) definition of

2105:

the sentence as a whole. I do know it's not grammatical. There are also the incomplete (?) sentence "Such ordering is well founded to," the phrase "Define we forcing," and other oddities. Would someone versed in this area mind taking a look? Thank you.

2638:

Mathematics loop. It appears that some editors have taken up the task of increasing the percentage by trying to break up this mathematics loop. This has resulted in some very contorted rewriting of the first sentences in these particular articles (see

3465:

As far as I see, it is possible to exterminate the word "series" from mathematics, but it is not worth to do, since ultimately it makes our language less convenient. This is not done for now, and I do not think this will happen in the (near) future.

3033:

Maybe an even better summary is his own (just above and below my one cited). He acknowledges that, first, he is "genetically" different from most of mathematicians. Second, that his adamant position did not change even a little after that discussion

2892:

or something that otherwise tells the lay reader that it's mathematics, then there's no need for the context-setting phrase and the phrase is probably just clutter then. Likewise often some other phrase in the opening sentence is sufficient and the

4129:

use the word "series". But examining calculus textbooks you can find maybe a dozen different - non equivalent - attempts to describe its meaning. All of them pretending to present THE meaning; no one mentions Tsirel's "We do not have a single...".

5506:

If you want to write an article on the history of the words "sequence" and "series" and submit it to a journal about the history of science, be my guest. None of this has anything to do with editing Knowledge, so please stop spamming it here.

4734: 2484:

I think the most egregious is edit warring at an established article to include a self-published fringe topic. The remainder may not pass the guidelines for inclusion in WP, but I leave that to the judgement of better-qualified Wikipedians.

2501:

a similar article for deletion, but that was years ago now and I don't remember if the content was similar. Looks to be cited to different "researchers" though. Could someone with the administrator tools check to see how similar these are?

1749:{\displaystyle 2\operatorname {cas} (a+b)=\operatorname {cas} (a)\operatorname {cas} (b)+\operatorname {cas} (-a)\operatorname {cas} (b)+\operatorname {cas} (a)\operatorname {cas} (-b)-\operatorname {cas} (-a)\operatorname {cas} (-b).\,} 5613:

None of your edits in the past couple of weeks relate in any identifiable way to the goal of informing WP readers about Cauchy's description of anything. Moreover, this is precisely the topic from which you are banned. Knock it off.

1364: 5872:

The mathematical notion usually named 'series' can be expressed/denoted by the symbolic form a1 + a2 + a3 + ··· . But equally well by the symbolic form a1 , a2 , a3 , ··· . The comma's-notation can be found in: A.R. Forsyth

3902: 3817: 6055:

I would be glad to convey the intuition behind "pointless spaces", too, but I cannot. This is beyond my competence. I never used such spaces in my research. I would be happy to have a coauthor able to enlarge this survey

2698:

I tend to concur with Bill. There are certain glitches in human nature, and sometimes it takes only a small persistent nudge to produce a large effect. In politics this is becoming a science. The existence of the

4350: 4406:

are functions (or operators, etc), there are often multiple common notions of convergence, so some care should be taken to indicate what's meant. This is all pretty standard; can we just drop this all now?

4072:

You are going to qualify this as being OR, not allowed in WP? It's nothing else than the observation that Cauchy's terminology (with his 'convergente' replaced by 'sommable') still fits with actual practice.

2770:,". The first link is not useful, as it duplicates the disambiguation in the title. Both links are too restricted, since ideals are used in many areas of mathematics. Therefore, a reader interested, say, in 4597: 3469:

Even if this seems helpful to do in textbooks, it is not. Textbooks should prepare a student to reading math literature. Thus, the word "series" (with all its intricacies) should be known to students.

2368: 3734: 3453: 63: 4857: 3613: 3249: 4906:

I invite everyone who criticizes my attempts to improve WP articles on 'series', to compare five sentences from Cauchy's text (1821) with Birkhoff's adapted (improved? modernized?) version (1973).

1766: 3525:"They say series, we should say series." — Indeed: "There's no free will," says the philosopher; "To hang is most unjust." "There is no free will," assents the officer; "We hang because we must." 3682: 5196: 1771: 4535: 2832:

example above. I don't know if it is possible to agree on a set of guidelines for arriving at the proper level of contextualization, but I do think it is something that should be discussed. --

3149:

Or maybe it is about abstract data types. To my regret, these are not defined and used in mathematics. It would be very convenient to define series as an abstract data type, in the spirit of

2812:

leave a lot of latitude for how contextualization is to be carried out (as they should, we don't want cookie-cutter articles) and all too often the simplest way to do it is to slap on an "In

6294: 6226: 2189: 6543:

Yes in fact that's how I discovered this red link. The google search with ""polynomial mapping" site:wikipedia.org" revels many potential link targets (so the topic is notable enough). --

6311: 6418: 6363: 2565: 5700: 1194: 1190: 1186: 1182: 1178: 1174: 1170: 1166: 1162: 1151: 1147: 1143: 1139: 1135: 1131: 1127: 1123: 1119: 1115: 1111: 1107: 1092: 1088: 1084: 1080: 1076: 1072: 1068: 1064: 1060: 1056: 1052: 1048: 1037: 1033: 1029: 1025: 1021: 1017: 1013: 1009: 1005: 1001: 997: 993: 982: 978: 974: 970: 966: 962: 958: 954: 950: 946: 942: 938: 927: 923: 919: 915: 911: 907: 903: 899: 895: 891: 887: 883: 872: 868: 864: 860: 856: 852: 848: 844: 840: 836: 832: 828: 817: 809: 805: 801: 797: 793: 789: 785: 781: 777: 773: 762: 758: 754: 750: 746: 742: 738: 734: 730: 726: 722: 718: 707: 703: 699: 695: 691: 687: 683: 679: 675: 671: 667: 663: 652: 648: 644: 640: 636: 632: 628: 624: 620: 616: 612: 608: 597: 593: 589: 585: 581: 577: 573: 569: 565: 561: 557: 553: 542: 538: 534: 530: 526: 522: 518: 514: 510: 506: 502: 498: 487: 483: 479: 475: 471: 467: 463: 459: 455: 451: 447: 443: 432: 428: 424: 420: 416: 412: 408: 404: 400: 396: 392: 388: 377: 373: 369: 365: 361: 357: 353: 349: 345: 341: 337: 333: 322: 318: 314: 310: 306: 302: 298: 294: 290: 286: 282: 278: 267: 263: 259: 255: 251: 247: 243: 239: 235: 231: 227: 223: 212: 208: 204: 200: 196: 192: 188: 184: 180: 176: 172: 168: 157: 153: 149: 145: 141: 137: 133: 129: 125: 121: 117: 113: 2413:

by Dominic Rochon and Pierre-Olivier Parisé to the attention of the more experienced editors in this group, since I'm not sure how this is most effectively managed. Please look at:

2257: 1335: 5882:

The same applies for the name of this notion: whether one says 'series' or 'infinite sequence with addable terms' or 'sequence with sum sequence', the notion does not change. --

4011: 3941: 2846:

I overstated the "categories" bit above, so acknowledging what others have said. Maybe a guideline should stay with "don't overdo it, but disambiguate context as appropriate". —

4785: 3973: 2386:

since 2012. About an animation which, in my opinion, is not really related to the subject, and disturbs reading. As I recommended in my last revert, a discussion has started at

6639: 3097:

This is very similar to what I also tried to articulate, only to find my wording picked apart, talked around in circles. Engaging with this editor is a pure waste of time.

1157: 1102: 1043: 988: 933: 878: 823: 768: 713: 658: 603: 548: 493: 438: 383: 328: 273: 218: 163: 108: 25: 3373: 3333: 2651:

and I and some others have been reverting these mangled attempts but we are at a loss as to whether there is anything more proactive that we could do. Suggestions welcome.

3283:

The language of "series" should not be interpreted literally; the meaning depends on the context; some mathematical maturity is needed in order to understand it correctly.

2607: 56: 5692: 3150: 2498: 5962: 5498: 4651: 3279: 2356: 102: 98: 94: 90: 4642: 4404: 4377: 6406:: "When a paper is published in viXra, it is usually a sign that it is not likely to contain acceptable results. It may, but the odds against that are considerable" 1553:{\displaystyle 2{\mbox{cas}}(a+b)={\mbox{cas}}(a){\mbox{cas}}(b)+{\mbox{cas}}(-a){\mbox{cas}}(b)+{\mbox{cas}}(a){\mbox{cas}}(-b)-{\mbox{cas}}(-a){\mbox{cas}}(-b).\,} 5521:

Agreed. I can't figure out what Hesselp is trying to accomplish here, or how it relates to editing the encyclopedia. It seems to be a lot of long-winded rambling.

6654: 21: 2534:

master thesis, or an older contribution of his master thesis advisor Rochon. The two web sites are those of these two authors. The account name of the author of

49: 2262:

It's of some interest to merge a historical remark like Tate curves. The module article is a bit terse and can use some expansion for instance by a merger. --

6217:

The problem is finding a Reliable Source (in the Knowledge definition of the term) that says in print what every physicist knows about it. I'll look around.

3251:

denotes just a number (the sum of the series), but sometimes it denotes something much more informative ("the whole series") that determines uniquely each

6595:

concerns a more general topic, I still think it makes sense to have a standalone article that doesn’t presuppose the readers know algebraic varieties. --

5772:

Idem, that the notion in question cannot be defined by "the operation of adding the terms" as well as by "a description of the operation of adding...." ?

2998:

German Knowledge. Now after his activities got largely stalled by other (math) editors in the German Knowledge, he seems to be back in the English one.--

5579:@JBL, @Reyk. Isn't it desirable to inform WP readers that Cauchy's description is an alternative for no definition at all (or five contradictory)? -- 6444: 6398: 6342: 2580: 2285: 2271: 1298:

I just did a quick spot-check of the mathematics textbooks I've got lying around, and most of them have gamma uncapitalised. So I would go with that.

2542:. This seems unrelated to the previous deleted article, as it is not cited in the new articles. I strongly suggest to delete the three new articles. 6522: 5953:

anything is said about the relevance of this argument. Or anything that touches this. I cannot find it; I suppose there's nothing of this kind. --

3824: 3739: 2881:" etc. can serve, but "In category theory" or "In functional analysis" cannot since they don't tell the lay reader that's it's about mathematics. 6569:. Also, a regular function on an affine algebraic variety is often called "polynomial function on the variety". Therefore, I suggest to redirect 4137: 17: 2725: 1206: 1202: 1198: 4379:

are numbers, this notation can generally denote either the series itself as a formal object, or the (ordinary) sum of the series. When the

2937: 2462: 2459: 2456: 4259: 2634:

Learning before entering the Knowledge ↔ Facts loop. One of the reasons that the percentage is not higher is due to the Mathematics -: -->

5774:

Idem, that "the operation of adding the terms" comes much closer to the notion 'summing a series' than to the notion 'series' itself? --

2465: 5485:

Birkhoff remarks in a footnote "Cauchy uses the word 'series' for 'sequence' and 'series' alike, ...". This is incorrect: Cauchy uses

4916: 6502:. So I’m planning to start the article if there is no good redirect target. (The definition in the finite-dimensional case appears in 3115:

Just a comment on how the "language of mathematics take these nuances into account": You seem to be discussing the difference between

2453: 2135: 4022:"having a sum". This double meaning has a long history, at least untill Euler and the Bernoullis. I cite (once more) Gauss, 18??: 6425: 6351: 3286:

This makes some troubles for teachers and students. Some students conclude that the series theory is non-rigorous, inconsistent etc.

1988:

Now I find that it looks correct when I'm logged out. As for preferences, I'm going to have to wait until tomorrow to look at that.

2194:

If I'm not mistaken, these are separate theories (and so a redirect is inappropriate.) I agree the page needs to be improved. --

1919:{\displaystyle {\begin{aligned}\cos(a+b)&=\cos a\cos b-\sin a\sin b\\\sin(a+b)&=\sin a\cos b+\cos a\sin b\end{aligned}}} 6592: 4555: 2700: 2629: 2276:

Sorry it seems the theory article discusses John Tate (not the theory) and so I simply redirected it to the module article. --

2078: 6282: 2449:

Several observations seem to apply: Multiple IPs from the same general location that could be the same person have been used:

2062:

is an orphan (i.e. no other articles link to it), cites no references, and is severely stubby. It may also have other issues.

6385: 6329: 6278: 6259: 6003: 3687: 3378: 3104: 2987: 4790: 3568: 3204: 2931: 2468: 5949:

You use "There is an admin discussion." as argument for undoing a revision on a talk page. Please mention here where in

3036:("you helped me to get my views on the subject even more concrete, and to find more compact and to-the-point wordings"), 2332: 6604: 6586: 6552: 6538: 6515: 6465: 6272: 6211: 6186: 6169: 6142: 6128: 6106: 6087: 6069: 6007: 5978: 5933: 5891: 5835: 5783: 5712: 5662: 5623: 5588: 5558: 5536: 5516: 4924: 4893: 4872: 4608: 4546: 4479: 4440: 4416: 4238: 3636: 3538: 3512: 3494: 3478: 3181: 3162: 3140: 3108: 3090: 3071: 3047: 3028: 3007: 2991: 2906: 2850: 2841: 2799: 2741: 2708: 2693: 2664: 2618: 2551: 2517: 2489: 2399: 2344: 2243: 2221: 2203: 2167: 2141: 2114: 2090: 2071: 2047: 1997: 1976: 1961: 1313: 1293: 1273: 1238: 4148:- a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after one ( 3458:

The question is, does it makes our language more convenient, or less convenient. I tried to consider some examples ("

4495: 3038:

in contrast to my position. Third, that there is, indeed, a chance that sometimes he will do according to my guess.

4107:). You varied the wordings of your two phrases in a way I never thought of. Combined with your puzzling "identify 3556:

Thanks to both of you for your efforts to explain your position, in a clear way. I'll make remarks on six points.

3124: 2331:

and various other mathematical articles, some members of this project may want to participate to the discussion at

6075: 4146:

Or, current practice in WP, present a handful of non-equivalent descriptions, pretending their equivalence? see:

5546: 4860: 5997: 3098: 2981: 1217: 5974: 1972: 6022: 2808:

for providing examples and clarifying (for me) what was nagging me about this construction. The guidelines in

2599: 2438: 6627: 6461: 6207: 5619: 5512: 4412: 3024: 2902: 2728:

encourages the same thing. I am curious, what peeves you about it? The grammatical construction? The use of

2720:, this sort of contextual link to the encompassing field is explicitly encouraged for technical articles in 2316: 2297: 2163: 2110: 2086: 2067: 1993: 1957: 1289: 1269: 6246: 6635: 6600: 6548: 6511: 4889: 4868: 4542: 4067: 3177: 3136: 3067: 2364: 2281: 2267: 2217: 2199: 2129: 2013: 5874: 2209: 2155: 2148: 6439: 6414: 6359: 6307: 6299: 6290: 6222: 6182: 2955: 2737: 2595: 2561: 2535: 2433: 2253: 2185: 2101: 1331: 6133:

No volunteers? A pity. For now, I wrote something... A competent coauthor is still welcome, of course.

5818:

Tsirel, on your judging "Cauchy's description" as a historical fact of no special importance nowadays:

3981: 3911: 6026: 3059: 2751:

what is exactly mathematics, for knowing if one may be interested in the article. Therefore, IMO, "In

6534: 6494:

is a red link. Is this topic covered somewhere? I think it would be unhelpful to just redirect it to

5542: 4739: 4645: 3949: 2324: 6076:

Knowledge-integrated: Appropriate material is integrated into Knowledge for added reach and exposure

5950: 4431:

And not a single citation backing up whatever the view is. Ignore or revert on sight is my opinion.

4024:

Die Convergenz einer Reihe an sich ist also wohl zu unterscheiden von der Convergenz ihrer Summirung

6620: 6591:

I agree with the definition. But shouldn’t the notion make sense outside algebraic geometry? Since

6503: 6499: 6157: 6153: 6018: 5970: 4729:{\displaystyle \sum _{-\infty }^{\infty }e^{2\pi in\bullet }=\sum _{-\infty }^{\infty }\delta _{n}} 4136:

should say series"? Should the WP article choose for just one description (out of the 'dozen')?

3116: 2943: 2783: 2759: 2174: 2025: 2006:

Here are screenshots of the above equations rendered by my Internet Explorer 11 with MathML and PNG

1983: 1968: 5985: 5954: 5883: 5827: 5775: 5654: 5580: 5490: 4471: 4230: 4018:

As is this capital-sigma form, the adjective ‘convergent’ is ambiguous as well: "having a limit"

3504: 2969: 2920: 2912: 6616: 6582: 6570: 6526: 6491: 6457: 6381: 6368: 6325: 6255: 6203: 5946: 5929: 5615: 5554: 5508: 4461:, I suppose? I agree, it wouldn't be possible to find reliable sources for his double cyclic: 4408: 4051: 3020: 2898: 2837: 2795: 2787: 2775: 2771: 2671: 2660: 2633:

Stopping at Philosophy is a bit arbitrary as any such path could be continued to Education -: -->

2614: 2547: 2395: 2340: 2328: 2159: 2106: 2082: 2063: 1989: 1953: 1285: 1265: 1223: 3338: 3298: 3198:

We do not have a singe, universally accepted (and rigorous, of course) definition of "a series".

2538:

is the same a the name of the web page of Parisé. This I agree that this is self publication of

6407: 2603: 2443: 6631: 6596: 6544: 6507: 5958: 5887: 5831: 5779: 5696: 5658: 5584: 5494: 4885: 4864: 4538: 4475: 4234: 3508: 3459: 3173: 3132: 3120: 3078: 3063: 3062:. (In case you thought this is a joke, actually I'm 1 percent serious about this concept.) -- 2925: 2847: 2705: 2577: 2486: 2410: 2387: 2360: 2277: 2263: 2213: 2195: 2125: 1355: 1351: 6574: 6566: 6558: 6451: 6434: 6410: 6403: 6393: 6355: 6337: 6303: 6286: 6267: 6218: 6178: 6165: 6138: 6124: 6102: 6083: 6065: 5708: 4604: 3534: 3474: 3169: 3158: 3086: 3043: 3003: 2977: 2767: 2733: 2648: 2557: 2423: 2249: 2181: 2043: 1327: 1221: 1219: 39: 3254: 6530: 6094: 4620: 4470:

In case you meant my text (22 Oct.), you probably missed Cauchy, Gauss, Bourbaki, EoM. --

4382: 4355: 3455:

of these two (interrelated) sequences. Other possibilities are also available, of course.

2809: 2721: 2059: 6285:

and such, but maybe there's something out there which is more suitable for our purposes.

2980:, where he has some novel ideas of his own. The situation could use close monitoring. 2778:

may think having followed a wrong link. Similarly, it is not clear from the title, that

6389: 6333: 6319:, which might pass as an expert's blog. Don't know who Briggs is though, so maybe not. 6263: 6112: 5756:

But (2): The 'five' refers (yes ?) to five actual descriptions in WP, summed up above

5529: 4436: 3490: 3128: 2758:

On the other hand, it is often unsuitable to use a too specific subfield. For example,

2686: 2510: 2236: 1306: 5821: 4141: 6648: 6578: 6377: 6321: 6251: 5993: 5925: 5921: 5550: 2833: 2805: 2791: 2656: 2610: 2543: 2427: 2391: 2336: 5192: 3526: 6562: 6529:. There is a brief definition there (a vector-valued polynomial in linear forms).-- 2539: 2383: 2376: 5880:. Whatever the choice of symbolic notation, the denoted notion remains the same. 6348: 6161: 6134: 6120: 6116: 6098: 6079: 6061: 5704: 4600: 3530: 3470: 3154: 3082: 3039: 3016: 2999: 2829: 2813: 2779: 2763: 2752: 2716: 2039: 5549:. I suggest to extend the ban to all pages and discussions where series occur. 1279:

Just to clarify a little, I noticed the vast majority of uses already in place

6495: 3897:{\displaystyle \textstyle \left((a_{n})\ ;\sum _{n=0}^{\ \infty }a_{n}\right)} 3812:{\displaystyle \textstyle \left((a_{n})\ ;\sum _{n=0}^{\ \infty }a_{n}\right)} 2312: 5747:

remarks on "A notion is, effectively, an equivalence class of definitions."

4026:, Werke, Abt.I, Band X, S.400. In all his publications Cauchy used the verb 6149: 5522: 4432: 3486: 2679: 2503: 2229: 2154:

One seldom sees a weaker attempt at a Knowledge article that the one called

1299: 1264:

An argument for capitalizing the initial "G" is that it's a capital Gamma.

5760:. How can you say that this five are 'not at all "contradictory"' ? For: 1322:

and spot-checking the books on my shelf, all the examples I find have the

2825: 2817: 4167: 4161: 4149: 4046:

Is this really true? Or do we overlook Cauchy's observation? His famous

1952:

Why is there that deficiency of space surrounding plus and minus signs?

4172:- a series is the sum of the terms of an infinite sequence of numbers ( 3151:

Equivalent definitions of mathematical structures#Mathematical practice

2821: 3621:

ways: the sum number, the sum sequence and the 'series' of sequence (

3503:

I'm working on a reaction on the last two edits (19 October 2017). --

4345:{\displaystyle a_{1}+a_{2}+a_{3}+\cdots =\sum _{n=1}^{\infty }a_{n}.} 2973: 2320: 2308: 2301: 1967:

It looks ok to me. What are your math rendering preferences set to? —

6302:

which notes that viXra is full of people who don't like relativity.

4173: 2248:

I don't think there's anything to merge; redirecting would be best.

4212:

se..., harmonic-se..., power-se..., trigonometric-se..., et cetera.

3630:

Bourbaki has, in editions 1942 until 1971, the distinctive forms:

2158:

in its current state. Can it be made into something worth keeping?

1937:

is even worse after the edit than before. Note that the spacing in

6372: 6195: 2828:

a branch of mathematics). But this can be taken too far as in the

2675: 2350:

Requested move: Permutation representation (disambiguation) -: -->

6317: 6243: 6240: 6237: 6234: 6231: 6111:

I boldly notify some experts that maybe rarely visit this page:

2212:” discuss the same stuff (and so I have suggested a merger.) —- 5489:

in all his works only for "an infinite sequence of reals". --

4901: 1224: 33: 2478: 6249:), etc... should tell you all you need to know about viXra. 4902:

G. Birkhoff's incorrect translation/interpretation of Cauchy

4034:

for summable, but this seems to be never adapted at large.

4592:{\displaystyle \textstyle \sum _{-\infty }^{\infty }a_{n}} 2726:

Knowledge:Manual_of_Style/Mathematics#Article_introduction

2315:. I have requested to revert an old move, that is to move 6060:

Who is ready to take this challenge? Thanks in advance.

6033:

The following sorts of spaces might be worth mentioning:

6029:

and refereed there. In the second referee report I read:

5820:

You think the same for Bourbaki's description (as in the

3119:, which appears in mathematics as the difference between 4919:; this adapted text is copied by J. Fauvel, J. Gray in 4206: 2972:

has started nibbling at the edges of his topic ban from

5757: 5751: 4467:

is an expression ....denoting either itself or its sum.

4458: 4104: 4100: 4066:", with 'quantity' = 'real number' as declared in 4044:

On "We do not have a single, universally accepted..."

3729:{\displaystyle \textstyle \sum _{n=0}^{\ \infty }a_{n}} 3448:{\displaystyle {\big (}(a_{n})_{n},(s_{n})_{n}{\big )}} 3012: 2961: 2949: 2644: 2640: 2572: 2418: 1254: 5253:

which succeed each other according to some fixed law.

4972:

which succeed each other according to some fixed law.

4559: 3985: 3953: 3915: 3828: 3743: 3691: 3640: 3572: 3208: 2576:, refraining from engaging on talk or edit comment. — 2474: 1527: 1508: 1486: 1470: 1451: 1432: 1413: 1397: 1372: 6347:

Well, he's the author of a book that's been reviewed

4852:{\displaystyle e^{2\pi in\bullet }={\widehat {f}}(n)} 4793: 4742: 4654: 4623: 4558: 4498: 4385: 4358: 4262: 3984: 3952: 3914: 3827: 3742: 3690: 3639: 3608:{\displaystyle \textstyle \sum _{n=1}^{\infty }a_{n}} 3571: 3462:", near the end), but he missed my point completely. 3381: 3341: 3301: 3257: 3244:{\displaystyle \textstyle \sum _{n=1}^{\infty }a_{n}} 3207: 1769: 1572: 1367: 4644:

there should be distributions or some other kind of

4099:

I looked again at your questions of 9 October 2017 (

2782:is about mathematics. This article begins with "In 2355:Participation to the move discussion is welcome at 5826:And for which out of the cited 'five' as well? -- 4851: 4779: 4728: 4636: 4591: 4529: 4398: 4371: 4344: 4005: 3967: 3935: 3896: 3811: 3728: 3677:{\displaystyle \textstyle _{n=0}^{\ \infty }a_{n}} 3676: 3607: 3447: 3367: 3327: 3273: 3243: 2608:Knowledge:Articles for deletion/Tricomplex numbers 1918: 1748: 1552: 1318:I can't recall seeing a text that capitalizes the 6626:I have proposed the move of the section title at 6456:your edits are a definite improvement, thanks. -- 5693:Equivalent definitions of mathematical structures 4648:. The example I had in mind was the formula like 4153:- a series, which is the operation of adding the 4062:. ("An infinite sequence of quantities is called 1945:is normal in the identities for sine and cosine. 6375:might be useful, although it's quite dated now. 2357:Talk:Permutation representation (disambiguation) 2081:, which seems to be on about the same level. -- 6433:already knows it isn't to be taken seriously. ~ 4530:{\displaystyle \sum _{-\infty }^{\infty }a_{n}} 4178:- a series is, ... an expression of the form Σ 1249:Is it the gamma function or the Gamma function? 5426:it is necessary and sufficiant that the sums 5255:These quantities themselves are the different 5129:it is necessary and sufficiant that the sums 4974:These quantities themselves are the different 3019:seems like a good summary of the situation. -- 2670:Meh. I just tried it now and got stuck in the 5743:@Boris Tsirelson. Again, I agree with your 4120:On "They say series, we should say series". 3460:User talk:Hesselp#Only a pedagogical problem? 3440: 3384: 1232:This page has archives. Sections older than 57: 8: 6630:. Opinions on the move are very welcome. -- 6557:As far as I know, a polynomial mapping is a 6504:Jacobian conjecture#The Jacobian determinant 3335:of its terms, or alternatively the sequence 3168:don’t know the best way to state/formulate 2208:On the other hand, i’m pretty sure it and “ 5994:WP:ANI#User:Hesselp violation of topic ban 4599:according to the distributional calculus? 4111:with...." I missed your point, yes indeed. 3081:; I suggested, he rejected (as usual...). 2824:) or if needed with a little assist (say, 64: 50: 5876:Theory of functions of a Complex Variable 4925:p.567, no digital version of this section 4829: 4828: 4798: 4792: 4747: 4741: 4720: 4710: 4702: 4677: 4667: 4659: 4653: 4628: 4622: 4582: 4572: 4564: 4557: 4521: 4511: 4503: 4497: 4390: 4384: 4363: 4357: 4333: 4323: 4312: 4293: 4280: 4267: 4261: 3993: 3983: 3958: 3951: 3923: 3913: 3882: 3870: 3859: 3841: 3826: 3797: 3785: 3774: 3756: 3741: 3719: 3707: 3696: 3689: 3667: 3655: 3644: 3638: 3598: 3588: 3577: 3570: 3439: 3438: 3432: 3422: 3406: 3396: 3383: 3382: 3380: 3359: 3349: 3340: 3319: 3309: 3300: 3262: 3256: 3234: 3224: 3213: 3206: 1770: 1768: 1571: 1526: 1507: 1485: 1469: 1450: 1431: 1412: 1396: 1371: 1366: 6523:Special:WhatLinksHere/Polynomial_mapping 5344:and the limit in question is called the 5060:and the limit in question is called the 4221:On "Bourbaki’s definition is absurd". 3554:On 'An opinion' (Boris Tsirelson, Dmcq) 2120:I've taken a quick look, but it needs a 3125:intensional, intuitionistic type theory 2732:instead of a more specific subfield? -- 2009: 1744: 1548: 88: 3194:Some truth lurks behind his position. 2390:, that requires third party opinions. 18:Knowledge talk:WikiProject Mathematics 6655:WikiProject Mathematics archives/2017 6245:(co-authored with the ever-wonderful 5353:By the principles established above, 5066:By the principles established above, 4097:On "he misses my point completely". 4014:, by abuse of language, if there is 7: 6042:Algebraic and Deligne–Mumford stacks 5920:I have asked for a ban extension at 4921:The History of Mathematics: A Reader 4060:une suite indéfinie de quantités ... 3821:The object symbolically denoted by 3079:User talk:Hesselp#Maybe I understand 4913:A Source Book in Classical Analysis 4909:A. Birkhoff's adapted translation 5541:This editor is banned for editing 4859:, the Fourier transformation (the 4711: 4706: 4668: 4663: 4573: 4568: 4512: 4507: 4324: 4006:{\displaystyle \textstyle (a_{n})} 3936:{\displaystyle \textstyle (a_{n})} 3873: 3788: 3710: 3658: 3589: 3225: 2323:. As this concerns, among others, 2077:FYI, the same editor also created 45:WikiProject Mathematics archives ( 32: 6426:Journal of Irreproducible Results 6074:And, by the way, that journal is 4132:So what do you, Dmcq, mean with " 4030:for limittable and the adjective 3946:the series whose general term is 3375:of its partial sums, or the pair 2473:Associated websites appear to be 2173:Should it maybe just redirect to 1236:may be automatically archived by 6525:there is one incoming link from 5766:for a notion cannot define that 5335:, then the series is said to be 5054:, then the series is said to be 4780:{\displaystyle \delta _{n}=f(n)} 4166:- a series is an infinite sum ( 3968:{\displaystyle \textstyle a_{n}} 2556:Yep, looks like self-promotion. 2388:Talk: Hypersurface#Animated plot 2024: 2012: 1284:to be more common this way). -- 38: 6593:morphism of algebraic varieties 5197:Bradley-Sandifer 2009 (English) 4457:@Dmcq. Your comment concerns 2888:If the title of the article is 2862:The reason for beginning with " 2701:Knowledge:Getting to Philosophy 2630:Knowledge:Getting to Philosophy 2409:I would like to bring possible 2079:Separating lattice homomorphism 6429:, with the difference is that 4846: 4840: 4822: 4816: 4774: 4768: 4759: 4753: 3999: 3986: 3929: 3916: 3904:, is verbally described by: 3847: 3834: 3762: 3749: 3617:This symbolic form is used in 3429: 3415: 3403: 3389: 3356: 3342: 3316: 3302: 2530:All of this is about Parisé's 1929:And the spacing deficiency in 1863: 1851: 1792: 1780: 1738: 1729: 1720: 1711: 1699: 1690: 1681: 1675: 1663: 1657: 1648: 1639: 1627: 1621: 1612: 1606: 1594: 1582: 1542: 1533: 1523: 1514: 1501: 1492: 1482: 1476: 1463: 1457: 1447: 1438: 1425: 1419: 1409: 1403: 1390: 1378: 1: 6641:23:03, 30 November 2017 (UTC) 6605:09:31, 30 November 2017 (UTC) 6587:08:44, 30 November 2017 (UTC) 6577:for clarifying the redirect. 6553:22:57, 29 November 2017 (UTC) 6539:21:55, 29 November 2017 (UTC) 6516:21:12, 29 November 2017 (UTC) 6466:18:25, 28 November 2017 (UTC) 6445:17:46, 28 November 2017 (UTC) 6419:16:53, 28 November 2017 (UTC) 6399:15:35, 28 November 2017 (UTC) 6364:15:29, 28 November 2017 (UTC) 6343:15:21, 28 November 2017 (UTC) 6312:15:21, 28 November 2017 (UTC) 6295:15:17, 28 November 2017 (UTC) 6277:It's easy to find chatter on 6273:15:15, 28 November 2017 (UTC) 6227:15:06, 28 November 2017 (UTC) 6212:13:10, 28 November 2017 (UTC) 6187:19:04, 24 November 2017 (UTC) 6170:06:33, 24 November 2017 (UTC) 6008:23:10, 22 November 2017 (UTC) 5762:Don't you agree with me that 4125:say series. Literally yes, 3182:18:56, 18 November 2017 (UTC) 3163:11:19, 18 November 2017 (UTC) 3141:23:12, 17 November 2017 (UTC) 2907:22:17, 17 November 2017 (UTC) 2851:03:22, 18 November 2017 (UTC) 2842:17:28, 17 November 2017 (UTC) 2800:15:37, 17 November 2017 (UTC) 2742:13:06, 17 November 2017 (UTC) 2709:12:40, 17 November 2017 (UTC) 2694:07:41, 17 November 2017 (UTC) 2665:03:41, 17 November 2017 (UTC) 2619:13:54, 16 November 2017 (UTC) 2581:03:32, 16 November 2017 (UTC) 2566:17:35, 15 November 2017 (UTC) 2552:12:46, 15 November 2017 (UTC) 2518:11:42, 15 November 2017 (UTC) 2490:02:25, 15 November 2017 (UTC) 2400:22:02, 15 November 2017 (UTC) 2382:A slow edit war has begun in 2370:20:30, 15 November 2017 (UTC) 2345:11:34, 15 November 2017 (UTC) 2286:03:06, 13 November 2017 (UTC) 2272:23:20, 12 November 2017 (UTC) 2258:17:26, 12 November 2017 (UTC) 2244:15:38, 12 November 2017 (UTC) 2222:15:36, 12 November 2017 (UTC) 6565:. See the first sentence of 6233:(from Jesus Christ himself)/ 6143:09:18, 7 November 2017 (UTC) 6129:07:20, 4 November 2017 (UTC) 6107:20:18, 3 November 2017 (UTC) 6088:19:04, 3 November 2017 (UTC) 6070:18:45, 3 November 2017 (UTC) 5979:01:26, 3 November 2017 (UTC) 5963:19:53, 2 November 2017 (UTC) 5951:WP's Policies and guidelines 5934:17:46, 30 October 2017 (UTC) 5892:20:21, 1 November 2017 (UTC) 5836:10:28, 31 October 2017 (UTC) 5784:10:03, 31 October 2017 (UTC) 5713:05:53, 31 October 2017 (UTC) 5663:15:33, 2 November 2017 (UTC) 5624:23:59, 30 October 2017 (UTC) 5589:17:25, 30 October 2017 (UTC) 5559:16:26, 30 October 2017 (UTC) 5537:16:17, 30 October 2017 (UTC) 5517:15:24, 30 October 2017 (UTC) 5499:15:13, 30 October 2017 (UTC) 4894:21:07, 28 October 2017 (UTC) 4873:00:21, 27 October 2017 (UTC) 4609:04:45, 25 October 2017 (UTC) 4547:04:00, 25 October 2017 (UTC) 4480:08:42, 24 October 2017 (UTC) 4441:20:55, 23 October 2017 (UTC) 4417:17:16, 22 October 2017 (UTC) 4239:15:29, 22 October 2017 (UTC) 3539:09:05, 21 October 2017 (UTC) 3513:13:35, 20 October 2017 (UTC) 3495:11:27, 19 October 2017 (UTC) 3479:10:15, 19 October 2017 (UTC) 3109:10:53, 16 October 2017 (UTC) 3091:05:40, 16 October 2017 (UTC) 3072:05:28, 16 October 2017 (UTC) 3048:18:04, 15 October 2017 (UTC) 3029:16:47, 15 October 2017 (UTC) 3008:14:23, 15 October 2017 (UTC) 2992:11:27, 15 October 2017 (UTC) 2637:Element (mathematics) -: --> 2333:Talk:Module (disambiguation) 2204:23:15, 9 November 2017 (UTC) 2190:16:46, 9 November 2017 (UTC) 2168:16:29, 9 November 2017 (UTC) 2142:21:28, 4 November 2017 (UTC) 2115:20:43, 4 November 2017 (UTC) 2091:21:24, 4 November 2017 (UTC) 2072:23:06, 3 November 2017 (UTC) 2048:19:54, 3 November 2017 (UTC) 1998:23:17, 27 October 2017 (UTC) 1977:22:49, 27 October 2017 (UTC) 1962:22:45, 27 October 2017 (UTC) 1336:03:56, 1 November 2017 (UTC) 1314:22:33, 31 October 2017 (UTC) 1294:22:28, 31 October 2017 (UTC) 1274:22:14, 31 October 2017 (UTC) 6567:Regular function#Definition 6154:Space (mathematics)#Schemes 5822:Encyclopedia of Mathematics 5185:B. Birkhoff's translation 4552:Rather intriguing: what is 3368:{\displaystyle (s_{n})_{n}} 3328:{\displaystyle (a_{n})_{n}} 6671: 6640:_Tannakian_formalism": --> 5471:converge to a fixed limit 5174:converge to a fixed limit 4224:WP Series (mathematics). 4081:On "Maybe he hopes..." . 3906:the series defined by the 2897:" incipit can be omitted. 2624:Getting to Philosophy game 2479:http://www.3dfractals.com/ 2351:Permutation representation 6158:Space (mathematics)#Topoi 5922:WP:ANI#User:Hesselp again 5547:Talk:Series (mathematics) 5331:for increasing values of 5327:tends to a certain limit 5050:for increasing values of 5046:tends to a certain limit 4861:Poisson summation formula 5310:be the sum of the first 5029:be the sum of the first 4168:Basic properties, line 1 2600:Tricomplex multibrot set 2439:Tricomplex multibrot set 2369:_Permutation_repre": --> 6628:Talk:Tannakian category 4016:no risk of confusion]. 2419:Very clear edit warring 2405:Self-publication on WP? 2317:Module (disambiguation) 2298:Module (disambiguation) 2058:The new article titled 6027:WikiJournal of Science 5988:violation of topic ban 4911:(see Garrett Birkhoff 4884:only unsupported). -- 4853: 4781: 4730: 4715: 4672: 4638: 4593: 4577: 4531: 4516: 4459:Deacon Vorbis, 22 Oct. 4400: 4373: 4346: 4328: 4207:section Series, line 1 4007: 3969: 3937: 3898: 3877: 3813: 3792: 3730: 3714: 3678: 3609: 3593: 3449: 3369: 3329: 3275: 3274:{\displaystyle a_{n}.} 3245: 3229: 3077:This is very close to 2890:Mathematical induction 2724:. Our manual of style 1920: 1750: 1563:I changed it to this: 1554: 1281:that I happened to see 1239:Lowercase sigmabot III 6423:It reminds me of the 6247:Florentin Smarandache 5340:(Cauchy: convergente) 4854: 4782: 4731: 4698: 4655: 4639: 4637:{\displaystyle a_{n}} 4594: 4560: 4532: 4499: 4401: 4399:{\displaystyle a_{n}} 4374: 4372:{\displaystyle a_{n}} 4347: 4308: 4160:one after the other ( 4140:? as in the renowned 4008: 3970: 3938: 3899: 3855: 3814: 3770: 3731: 3692: 3679: 3610: 3573: 3450: 3370: 3330: 3276: 3246: 3209: 2102:Forcing (mathematics) 1921: 1751: 1555: 6573:there, and to adapt 5758:almost at the end of 5543:Series (mathematics) 5210:(Cauchy: On appelle 5193:Cauchy 1821 (French) 4791: 4740: 4652: 4646:generalized function 4621: 4556: 4496: 4383: 4356: 4260: 3982: 3950: 3912: 3825: 3740: 3688: 3637: 3569: 3379: 3339: 3299: 3255: 3205: 3123:(as in Martin-Lof's 2325:Module (mathematics) 1767: 1570: 1365: 6621:Tannakian formalism 6500:polynomial function 6148:A lot of thanks to 6019:Space (mathematics) 5207:is used as name for 3662: 3117:sense and reference 2784:homological algebra 2760:Ideal (ring theory) 2628:Consider the essay 2475:http://mathopo.com/ 2097:Copy editing needed 1358:I found this line: 6617:Tannakian category 6571:polynomial mapping 6527:Polynomial functor 6492:polynomial mapping 6490:Hi all. I noticed 6486:Polynomial mapping 6177:Very nice work! -- 6095:v:User talk:Tsirel 4849: 4777: 4726: 4634: 4589: 4588: 4527: 4396: 4369: 4342: 4003: 4002: 3965: 3964: 3933: 3932: 3894: 3893: 3809: 3808: 3726: 3725: 3674: 3673: 3641: 3605: 3604: 3445: 3365: 3325: 3271: 3241: 3240: 2788:algebraic geometry 2776:algebraic geometry 2772:algebraic geometry 2755:," is overlinking. 2672:Cardinal direction 2596:Tricomplex numbers 2536:Tricomplex numbers 2434:Tricomplex numbers 2329:Modular arithmetic 2178:-adic Hodge theory 1916: 1914: 1746: 1745: 1550: 1549: 1531: 1512: 1490: 1474: 1455: 1436: 1417: 1401: 1376: 6443: 5697:topological space 5483:any explanation. 5350: 5341: 5318:is some integer. 5222: 5215: 5200: 5037:is some integer. 4928: 4837: 4256:is an expression 4068:PRÉLIMINAIRES p.2 4052:CHAPITRE VI p.123 3872: 3851: 3787: 3766: 3709: 3657: 3129:extensional logic 3121:intensional logic 3037: 2976:, at the article 2606:for deletion. See 2594:I have nominated 2573:pretty determined 2210:Hodge–Tate module 2156:Hodge–Tate theory 2149:Hodge–Tate theory 1530: 1511: 1489: 1473: 1454: 1435: 1416: 1400: 1375: 1356:Hartley transform 1346:"cas" typesetting 1246: 1245: 95:Nov 2002–Dec 2003 6662: 6575:regular function 6559:regular function 6455: 6437: 6397: 6341: 6271: 6039:Algebraic spaces 6000: 5527: 5348: 5339: 5220: 5209: 5190: 5189:his adaptations 4910: 4858: 4856: 4855: 4850: 4839: 4838: 4830: 4815: 4814: 4786: 4784: 4783: 4778: 4752: 4751: 4735: 4733: 4732: 4727: 4725: 4724: 4714: 4709: 4694: 4693: 4671: 4666: 4643: 4641: 4640: 4635: 4633: 4632: 4598: 4596: 4595: 4590: 4587: 4586: 4576: 4571: 4536: 4534: 4533: 4528: 4526: 4525: 4515: 4510: 4405: 4403: 4402: 4397: 4395: 4394: 4378: 4376: 4375: 4370: 4368: 4367: 4351: 4349: 4348: 4343: 4338: 4337: 4327: 4322: 4298: 4297: 4285: 4284: 4272: 4271: 4012: 4010: 4009: 4004: 3998: 3997: 3974: 3972: 3971: 3966: 3963: 3962: 3942: 3940: 3939: 3934: 3928: 3927: 3903: 3901: 3900: 3895: 3892: 3888: 3887: 3886: 3876: 3871: 3869: 3850: 3846: 3845: 3818: 3816: 3815: 3810: 3807: 3803: 3802: 3801: 3791: 3786: 3784: 3765: 3761: 3760: 3735: 3733: 3732: 3727: 3724: 3723: 3713: 3708: 3706: 3683: 3681: 3680: 3675: 3672: 3671: 3661: 3656: 3654: 3614: 3612: 3611: 3606: 3603: 3602: 3592: 3587: 3527:q:Ambrose_Bierce 3454: 3452: 3451: 3446: 3444: 3443: 3437: 3436: 3427: 3426: 3411: 3410: 3401: 3400: 3388: 3387: 3374: 3372: 3371: 3366: 3364: 3363: 3354: 3353: 3334: 3332: 3331: 3326: 3324: 3323: 3314: 3313: 3280: 3278: 3277: 3272: 3267: 3266: 3250: 3248: 3247: 3242: 3239: 3238: 3228: 3223: 3170:geometric series 3101: 3060:motivic calculus 3035: 2984: 2978:Cesaro summation 2965: 2938:deleted contribs 2873:Alternatively, " 2834:Bill Cherowitzo 2768:abstract algebra 2762:begins with "In 2684: 2657:Bill Cherowitzo 2575: 2508: 2424:Bicomplex number 2421: 2411:self-publication 2234: 2138: 2132: 2028: 2016: 1987: 1925: 1923: 1922: 1917: 1915: 1755: 1753: 1752: 1747: 1559: 1557: 1556: 1551: 1532: 1528: 1513: 1509: 1491: 1487: 1475: 1471: 1456: 1452: 1437: 1433: 1418: 1414: 1402: 1398: 1377: 1373: 1304: 1241: 1225: 66: 59: 52: 42: 34: 6670: 6669: 6665: 6664: 6663: 6661: 6660: 6659: 6645: 6644: 6624: 6615:Proposed move: 6488: 6449: 6404:Gerard 't Hooft 6376: 6320: 6250: 6199: 6162:Boris Tsirelson 6135:Boris Tsirelson 6121:Boris Tsirelson 6099:Boris Tsirelson 6080:Boris Tsirelson 6062:Boris Tsirelson 6015: 6013:Coauthor needed 5998: 5990: 5705:Boris Tsirelson 5695:. For example, 5533: 5523: 5470: 5460: 5453: 5446: 5439: 5431: 5419: 5414: 5405: 5399: 5390: 5385: 5379: 5374: 5368: 5363: 5351:of the series. 5349:(Cauchy: somme) 5325: 5309: 5299: 5292: 5285: 5278: 5270: 5250: 5243: 5236: 5229: 5221:(Cauchy: suite) 5173: 5163: 5156: 5149: 5142: 5134: 5119: 5106: 5094: 5085: 5076: 5064:of the series. 5044: 5028: 5018: 5011: 5004: 4997: 4989: 4969: 4962: 4955: 4948: 4904: 4794: 4789: 4788: 4743: 4738: 4737: 4716: 4673: 4650: 4649: 4624: 4619: 4618: 4601:Boris Tsirelson 4578: 4554: 4553: 4517: 4494: 4493: 4386: 4381: 4380: 4359: 4354: 4353: 4329: 4289: 4276: 4263: 4258: 4257: 4204: 4197: 4189: 4184: 4158: 4048:Cours d'Analyse 3989: 3980: 3979: 3954: 3948: 3947: 3919: 3910: 3909: 3878: 3837: 3833: 3829: 3823: 3822: 3793: 3752: 3748: 3744: 3738: 3737: 3715: 3686: 3685: 3663: 3635: 3634: 3633: 3626: 3594: 3567: 3566: 3565:On "Sometimes 3531:Boris Tsirelson 3471:Boris Tsirelson 3428: 3418: 3402: 3392: 3377: 3376: 3355: 3345: 3337: 3336: 3315: 3305: 3297: 3296: 3258: 3253: 3252: 3230: 3203: 3202: 3192: 3155:Boris Tsirelson 3099: 3083:Boris Tsirelson 3040:Boris Tsirelson 2982: 2923: 2917: 2864:In mathematics, 2810:MOS:CONTEXTLINK 2722:MOS:CONTEXTLINK 2690: 2680: 2636:Counting -: --> 2635:Quantity -: --> 2626: 2571: 2514: 2504: 2417: 2407: 2380: 2353: 2305: 2296:Requested move 2240: 2230: 2152: 2136: 2130: 2099: 2060:Minimal algebra 2056: 2054:Minimal algebra 2032: 2029: 2020: 2017: 1981: 1913: 1912: 1866: 1842: 1841: 1795: 1765: 1764: 1568: 1567: 1363: 1362: 1348: 1310: 1300: 1251: 1237: 1226: 1220: 1211: 1097: 87: 86: 73: 70: 30: 29: 28: 12: 11: 5: 6668: 6666: 6658: 6657: 6647: 6646: 6623: 6613: 6612: 6611: 6610: 6609: 6608: 6607: 6541: 6487: 6484: 6483: 6482: 6481: 6480: 6479: 6478: 6477: 6476: 6475: 6474: 6473: 6472: 6471: 6470: 6469: 6468: 6275: 6229: 6198: 6193: 6192: 6191: 6190: 6189: 6146: 6113:User:John Baez 6058: 6057: 6049: 6048: 6047: 6046: 6043: 6040: 6037: 6014: 6011: 5999:Sławomir Biały 5989: 5983: 5982: 5981: 5971:David Eppstein 5943: 5942: 5941: 5940: 5939: 5938: 5937: 5936: 5911: 5910: 5909: 5908: 5907: 5906: 5905: 5904: 5903: 5902: 5901: 5900: 5899: 5898: 5897: 5896: 5895: 5894: 5881: 5878:, 1918 page 21 5853: 5852: 5851: 5850: 5849: 5848: 5847: 5846: 5845: 5844: 5843: 5842: 5841: 5840: 5839: 5838: 5825: 5819: 5801: 5800: 5799: 5798: 5797: 5796: 5795: 5794: 5793: 5792: 5791: 5790: 5789: 5788: 5787: 5786: 5773: 5771: 5761: 5755: 5748: 5726: 5725: 5724: 5723: 5722: 5721: 5720: 5719: 5718: 5717: 5716: 5715: 5678: 5677: 5676: 5675: 5674: 5673: 5672: 5671: 5670: 5669: 5668: 5667: 5666: 5665: 5637: 5636: 5635: 5634: 5633: 5632: 5631: 5630: 5629: 5628: 5627: 5626: 5600: 5599: 5598: 5597: 5596: 5595: 5594: 5593: 5592: 5591: 5568: 5567: 5566: 5565: 5564: 5563: 5562: 5561: 5531: 5484: 5465: 5458: 5451: 5444: 5437: 5429: 5425: 5415: 5409: 5401: 5397: 5386: 5383: 5375: 5372: 5364: 5361: 5352: 5343: 5323: 5319: 5304: 5297: 5290: 5283: 5276: 5268: 5264: 5254: 5252: 5248: 5241: 5234: 5227: 5223:of quantities 5202: 5168: 5161: 5154: 5147: 5140: 5132: 5128: 5114: 5104: 5092: 5083: 5074: 5065: 5059: 5042: 5038: 5023: 5016: 5009: 5002: 4995: 4987: 4983: 4973: 4971: 4967: 4960: 4953: 4946: 4942:of quantities 4930: 4903: 4900: 4899: 4898: 4897: 4896: 4878: 4877: 4876: 4875: 4848: 4845: 4842: 4836: 4833: 4827: 4824: 4821: 4818: 4813: 4810: 4807: 4804: 4801: 4797: 4776: 4773: 4770: 4767: 4764: 4761: 4758: 4755: 4750: 4746: 4723: 4719: 4713: 4708: 4705: 4701: 4697: 4692: 4689: 4686: 4683: 4680: 4676: 4670: 4665: 4662: 4658: 4631: 4627: 4612: 4611: 4585: 4581: 4575: 4570: 4567: 4563: 4524: 4520: 4514: 4509: 4506: 4502: 4489: 4488: 4487: 4486: 4485: 4484: 4483: 4482: 4469: 4448: 4447: 4446: 4445: 4444: 4443: 4424: 4423: 4422: 4421: 4420: 4419: 4393: 4389: 4366: 4362: 4341: 4336: 4332: 4326: 4321: 4318: 4315: 4311: 4307: 4304: 4301: 4296: 4292: 4288: 4283: 4279: 4275: 4270: 4266: 4244: 4243: 4242: 4241: 4228: 4225: 4222: 4216: 4215: 4214: 4213: 4210: 4202: 4195: 4187: 4179: 4177: 4171: 4165: 4156: 4152: 4147: 4145: 4131: 4121: 4115: 4114: 4113: 4112: 4098: 4092: 4091: 4090: 4089: 4082: 4076: 4075: 4074: 4073: 4071: 4045: 4039: 4038: 4037: 4036: 4035: 4017: 4015: 4001: 3996: 3992: 3988: 3961: 3957: 3931: 3926: 3922: 3918: 3907: 3891: 3885: 3881: 3875: 3868: 3865: 3862: 3858: 3854: 3849: 3844: 3840: 3836: 3832: 3820: 3806: 3800: 3796: 3790: 3783: 3780: 3777: 3773: 3769: 3764: 3759: 3755: 3751: 3747: 3722: 3718: 3712: 3705: 3702: 3699: 3695: 3670: 3666: 3660: 3653: 3650: 3647: 3643: 3631: 3629: 3624: 3616: 3601: 3597: 3591: 3586: 3583: 3580: 3576: 3560: 3559: 3558: 3557: 3555: 3548: 3546: 3545: 3544: 3543: 3542: 3541: 3518: 3517: 3516: 3515: 3498: 3497: 3442: 3435: 3431: 3425: 3421: 3417: 3414: 3409: 3405: 3399: 3395: 3391: 3386: 3362: 3358: 3352: 3348: 3344: 3322: 3318: 3312: 3308: 3304: 3288: 3287: 3284: 3281: 3270: 3265: 3261: 3237: 3233: 3227: 3222: 3219: 3216: 3212: 3199: 3191: 3188: 3187: 3186: 3185: 3184: 3165: 3144: 3143: 3112: 3111: 3100:Sławomir Biały 3094: 3093: 3055: 3054: 3053: 3052: 3051: 3050: 2983:Sławomir Biały 2967: 2966: 2916: 2910: 2886: 2885: 2871: 2870: 2860: 2859: 2858: 2857: 2856: 2855: 2854: 2853: 2766:, a branch of 2756: 2745: 2744: 2713:Regarding the 2711: 2696: 2688: 2625: 2622: 2592: 2591: 2590: 2589: 2588: 2587: 2586: 2585: 2584: 2583: 2523: 2522: 2521: 2520: 2512: 2482: 2481: 2471: 2463:142.169.78.111 2460:132.209.100.23 2457:142.169.78.184 2447: 2446: 2441: 2436: 2431: 2406: 2403: 2379: 2373: 2352: 2348: 2304: 2294: 2293: 2292: 2291: 2290: 2289: 2288: 2274: 2238: 2225: 2224: 2206: 2192: 2151: 2146: 2145: 2144: 2098: 2095: 2094: 2093: 2055: 2052: 2051: 2050: 2034: 2033: 2030: 2023: 2021: 2018: 2011: 2008: 2007: 2003: 2002: 2001: 2000: 1984:David Eppstein 1969:David Eppstein 1950: 1949: 1927: 1926: 1911: 1908: 1905: 1902: 1899: 1896: 1893: 1890: 1887: 1884: 1881: 1878: 1875: 1872: 1869: 1867: 1865: 1862: 1859: 1856: 1853: 1850: 1847: 1844: 1843: 1840: 1837: 1834: 1831: 1828: 1825: 1822: 1819: 1816: 1813: 1810: 1807: 1804: 1801: 1798: 1796: 1794: 1791: 1788: 1785: 1782: 1779: 1776: 1773: 1772: 1757: 1756: 1743: 1740: 1737: 1734: 1731: 1728: 1725: 1722: 1719: 1716: 1713: 1710: 1707: 1704: 1701: 1698: 1695: 1692: 1689: 1686: 1683: 1680: 1677: 1674: 1671: 1668: 1665: 1662: 1659: 1656: 1653: 1650: 1647: 1644: 1641: 1638: 1635: 1632: 1629: 1626: 1623: 1620: 1617: 1614: 1611: 1608: 1605: 1602: 1599: 1596: 1593: 1590: 1587: 1584: 1581: 1578: 1575: 1561: 1560: 1547: 1544: 1541: 1538: 1535: 1525: 1522: 1519: 1516: 1506: 1503: 1500: 1497: 1494: 1484: 1481: 1478: 1468: 1465: 1462: 1459: 1449: 1446: 1443: 1440: 1430: 1427: 1424: 1421: 1411: 1408: 1405: 1395: 1392: 1389: 1386: 1383: 1380: 1370: 1347: 1344: 1343: 1342: 1341: 1340: 1339: 1338: 1308: 1262: 1261: 1250: 1247: 1244: 1243: 1231: 1228: 1227: 1222: 1218: 1216: 1213: 1212: 1210: 1209: 1154: 1098: 1096: 1095: 1040: 985: 930: 875: 820: 765: 710: 655: 600: 545: 490: 435: 380: 325: 270: 215: 160: 105: 84: 83: 82: 79: 78: 75: 74: 69: 68: 61: 54: 46: 43: 37: 31: 15: 14: 13: 10: 9: 6: 4: 3: 2: 6667: 6656: 6653: 6652: 6650: 6643: 6642: 6637: 6633: 6629: 6622: 6618: 6614: 6606: 6602: 6598: 6594: 6590: 6589: 6588: 6584: 6580: 6576: 6572: 6568: 6564: 6563:affine spaces 6560: 6556: 6555: 6554: 6550: 6546: 6542: 6540: 6536: 6532: 6528: 6524: 6520: 6519: 6518: 6517: 6513: 6509: 6505: 6501: 6497: 6493: 6485: 6467: 6463: 6459: 6453: 6448: 6447: 6446: 6441: 6436: 6432: 6428: 6427: 6422: 6421: 6420: 6416: 6412: 6408: 6405: 6402: 6401: 6400: 6395: 6391: 6387: 6383: 6379: 6374: 6370: 6367: 6366: 6365: 6361: 6357: 6353: 6350: 6346: 6345: 6344: 6339: 6335: 6331: 6327: 6323: 6318: 6316:There's also 6315: 6314: 6313: 6309: 6305: 6301: 6298: 6297: 6296: 6292: 6288: 6284: 6280: 6276: 6274: 6269: 6265: 6261: 6257: 6253: 6248: 6244: 6241: 6238: 6235: 6232: 6230: 6228: 6224: 6220: 6216: 6215: 6214: 6213: 6209: 6205: 6197: 6194: 6188: 6184: 6180: 6176: 6175: 6174: 6173: 6172: 6171: 6167: 6163: 6159: 6155: 6151: 6145: 6144: 6140: 6136: 6131: 6130: 6126: 6122: 6118: 6114: 6109: 6108: 6104: 6100: 6096: 6090: 6089: 6085: 6081: 6077: 6072: 6071: 6067: 6063: 6054: 6053: 6052: 6044: 6041: 6038: 6035: 6034: 6032: 6031: 6030: 6028: 6024: 6020: 6012: 6010: 6009: 6005: 6001: 5995: 5987: 5984: 5980: 5976: 5972: 5967: 5966: 5965: 5964: 5960: 5956: 5952: 5948: 5947:Limit-theorem 5935: 5931: 5927: 5923: 5919: 5918: 5917: 5916: 5915: 5914: 5913: 5912: 5893: 5889: 5885: 5879: 5877: 5871: 5870: 5869: 5868: 5867: 5866: 5865: 5864: 5863: 5862: 5861: 5860: 5859: 5858: 5857: 5856: 5855: 5854: 5837: 5833: 5829: 5823: 5817: 5816: 5815: 5814: 5813: 5812: 5811: 5810: 5809: 5808: 5807: 5806: 5805: 5804: 5803: 5802: 5785: 5781: 5777: 5769: 5768:notion itself 5765: 5764:an expression 5759: 5753: 5746: 5742: 5741: 5740: 5739: 5738: 5737: 5736: 5735: 5734: 5733: 5732: 5731: 5730: 5729: 5728: 5727: 5714: 5710: 5706: 5702: 5701:7 definitions 5699:has at least 5698: 5694: 5690: 5689: 5688: 5687: 5686: 5685: 5684: 5683: 5682: 5681: 5680: 5679: 5664: 5660: 5656: 5651: 5650: 5649: 5648: 5647: 5646: 5645: 5644: 5643: 5642: 5641: 5640: 5639: 5638: 5625: 5621: 5617: 5612: 5611: 5610: 5609: 5608: 5607: 5606: 5605: 5604: 5603: 5602: 5601: 5590: 5586: 5582: 5578: 5577: 5576: 5575: 5574: 5573: 5572: 5571: 5570: 5569: 5560: 5556: 5552: 5548: 5544: 5540: 5539: 5538: 5535: 5534: 5528: 5526: 5520: 5519: 5518: 5514: 5510: 5505: 5504: 5503: 5502: 5501: 5500: 5496: 5492: 5488: 5480: 5478: 5474: 5468: 5464: 5457: 5450: 5443: 5436: 5432: 5423: 5422:be convergent 5418: 5412: 5408: 5404: 5400: 5394: 5389: 5382: 5378: 5371: 5367: 5360: 5357:the series 5356: 5355:in order that 5347: 5338: 5334: 5330: 5326: 5317: 5314:terms, where 5313: 5307: 5303: 5296: 5289: 5282: 5275: 5271: 5262: 5258: 5247: 5240: 5233: 5226: 5219: 5213: 5208: 5206: 5198: 5194: 5188: 5183: 5181: 5177: 5171: 5167: 5160: 5153: 5146: 5139: 5135: 5126: 5122: 5117: 5113: 5110: 5107: 5101: 5097: 5091: 5088: 5082: 5079: 5073: 5070:the series 5069: 5063: 5057: 5053: 5049: 5045: 5036: 5033:terms, where 5032: 5026: 5022: 5015: 5008: 5001: 4994: 4990: 4981: 4977: 4966: 4959: 4952: 4945: 4941: 4937: 4935: 4926: 4922: 4918: 4914: 4907: 4895: 4891: 4887: 4882: 4881: 4880: 4879: 4874: 4870: 4866: 4862: 4843: 4834: 4831: 4825: 4819: 4811: 4808: 4805: 4802: 4799: 4795: 4771: 4765: 4762: 4756: 4748: 4744: 4721: 4717: 4703: 4699: 4695: 4690: 4687: 4684: 4681: 4678: 4674: 4660: 4656: 4647: 4629: 4625: 4616: 4615: 4614: 4613: 4610: 4606: 4602: 4583: 4579: 4565: 4561: 4551: 4550: 4549: 4548: 4544: 4540: 4522: 4518: 4504: 4500: 4481: 4477: 4473: 4468: 4464: 4460: 4456: 4455: 4454: 4453: 4452: 4451: 4450: 4449: 4442: 4438: 4434: 4430: 4429: 4428: 4427: 4426: 4425: 4418: 4414: 4410: 4409:Deacon Vorbis 4391: 4387: 4364: 4360: 4339: 4334: 4330: 4319: 4316: 4313: 4309: 4305: 4302: 4299: 4294: 4290: 4286: 4281: 4277: 4273: 4268: 4264: 4255: 4250: 4249: 4248: 4247: 4246: 4245: 4240: 4236: 4232: 4220: 4219: 4218: 4217: 4208: 4201: 4194: 4190: 4182: 4175: 4169: 4163: 4159: 4150: 4143: 4139: 4135: 4128: 4124: 4119: 4118: 4117: 4116: 4110: 4106: 4102: 4096: 4095: 4094: 4093: 4086: 4080: 4079: 4078: 4077: 4069: 4065: 4061: 4057: 4054:simply with: 4053: 4049: 4043: 4042: 4041: 4040: 4033: 4029: 4025: 4021: 4013: 3994: 3990: 3975: 3959: 3955: 3943: 3924: 3920: 3889: 3883: 3879: 3866: 3863: 3860: 3856: 3852: 3842: 3838: 3830: 3804: 3798: 3794: 3781: 3778: 3775: 3771: 3767: 3757: 3753: 3745: 3720: 3716: 3703: 3700: 3697: 3693: 3668: 3664: 3651: 3648: 3645: 3642: 3627: 3620: 3615:denotes ..." 3599: 3595: 3584: 3581: 3578: 3574: 3564: 3563: 3562: 3561: 3553: 3552: 3551: 3550: 3549: 3540: 3536: 3532: 3528: 3524: 3523: 3522: 3521: 3520: 3519: 3514: 3510: 3506: 3502: 3501: 3500: 3499: 3496: 3492: 3488: 3483: 3482: 3481: 3480: 3476: 3472: 3467: 3463: 3461: 3456: 3433: 3423: 3419: 3412: 3407: 3397: 3393: 3360: 3350: 3346: 3320: 3310: 3306: 3292: 3285: 3282: 3268: 3263: 3259: 3235: 3231: 3220: 3217: 3214: 3210: 3200: 3197: 3196: 3195: 3189: 3183: 3179: 3175: 3171: 3166: 3164: 3160: 3156: 3152: 3148: 3147: 3146: 3145: 3142: 3138: 3134: 3130: 3126: 3122: 3118: 3114: 3113: 3110: 3106: 3102: 3096: 3095: 3092: 3088: 3084: 3080: 3076: 3075: 3074: 3073: 3069: 3065: 3061: 3049: 3045: 3041: 3032: 3031: 3030: 3026: 3022: 3018: 3014: 3011: 3010: 3009: 3005: 3001: 2996: 2995: 2994: 2993: 2989: 2985: 2979: 2975: 2971: 2963: 2960: 2957: 2954: 2951: 2948: 2945: 2942: 2939: 2936: 2933: 2930: 2927: 2922: 2919: 2918: 2914: 2911: 2909: 2908: 2904: 2900: 2899:Michael Hardy 2896: 2891: 2884: 2883: 2882: 2880: 2876: 2869: 2868: 2867: 2865: 2852: 2849: 2845: 2844: 2843: 2839: 2835: 2831: 2827: 2823: 2819: 2815: 2811: 2807: 2804:My thanks to 2803: 2802: 2801: 2797: 2793: 2789: 2785: 2781: 2777: 2773: 2769: 2765: 2761: 2757: 2754: 2749: 2748: 2747: 2746: 2743: 2739: 2735: 2731: 2727: 2723: 2719: 2718: 2712: 2710: 2707: 2702: 2697: 2695: 2692: 2691: 2685: 2683: 2677: 2673: 2669: 2668: 2667: 2666: 2662: 2658: 2652: 2650: 2646: 2642: 2631: 2623: 2621: 2620: 2616: 2612: 2609: 2605: 2601: 2597: 2582: 2579: 2574: 2569: 2568: 2567: 2563: 2559: 2555: 2554: 2553: 2549: 2545: 2541: 2537: 2533: 2529: 2528: 2527: 2526: 2525: 2524: 2519: 2516: 2515: 2509: 2507: 2500: 2496: 2495: 2494: 2493: 2492: 2491: 2488: 2480: 2476: 2472: 2470: 2467: 2466:142.169.78.50 2464: 2461: 2458: 2455: 2452: 2451: 2450: 2445: 2442: 2440: 2437: 2435: 2432: 2429: 2425: 2420: 2416: 2415: 2414: 2412: 2404: 2402: 2401: 2397: 2393: 2389: 2385: 2378: 2375:Animation in 2374: 2372: 2371: 2366: 2362: 2358: 2349: 2347: 2346: 2342: 2338: 2334: 2330: 2326: 2322: 2318: 2314: 2311:redirects to 2310: 2303: 2299: 2295: 2287: 2283: 2279: 2275: 2273: 2269: 2265: 2261: 2260: 2259: 2255: 2251: 2247: 2246: 2245: 2242: 2241: 2235: 2233: 2227: 2226: 2223: 2219: 2215: 2211: 2207: 2205: 2201: 2197: 2193: 2191: 2187: 2183: 2179: 2177: 2172: 2171: 2170: 2169: 2165: 2161: 2160:Michael Hardy 2157: 2150: 2147: 2143: 2139: 2133: 2127: 2123: 2119: 2118: 2117: 2116: 2112: 2108: 2107:Jessicapierce 2103: 2096: 2092: 2088: 2084: 2083:Deacon Vorbis 2080: 2076: 2075: 2074: 2073: 2069: 2065: 2064:Michael Hardy 2061: 2053: 2049: 2045: 2041: 2036: 2035: 2027: 2022: 2015: 2010: 2005: 2004: 1999: 1995: 1991: 1990:Michael Hardy 1985: 1980: 1979: 1978: 1974: 1970: 1966: 1965: 1964: 1963: 1959: 1955: 1954:Michael Hardy 1948: 1947: 1946: 1944: 1940: 1936: 1932: 1909: 1906: 1903: 1900: 1897: 1894: 1891: 1888: 1885: 1882: 1879: 1876: 1873: 1870: 1868: 1860: 1857: 1854: 1848: 1845: 1838: 1835: 1832: 1829: 1826: 1823: 1820: 1817: 1814: 1811: 1808: 1805: 1802: 1799: 1797: 1789: 1786: 1783: 1777: 1774: 1763: 1762: 1761: 1741: 1735: 1732: 1726: 1723: 1717: 1714: 1708: 1705: 1702: 1696: 1693: 1687: 1684: 1678: 1672: 1669: 1666: 1660: 1654: 1651: 1645: 1642: 1636: 1633: 1630: 1624: 1618: 1615: 1609: 1603: 1600: 1597: 1591: 1588: 1585: 1579: 1576: 1573: 1566: 1565: 1564: 1545: 1539: 1536: 1520: 1517: 1504: 1498: 1495: 1479: 1466: 1460: 1444: 1441: 1428: 1422: 1406: 1393: 1387: 1384: 1381: 1368: 1361: 1360: 1359: 1357: 1353: 1345: 1337: 1333: 1329: 1325: 1321: 1317: 1316: 1315: 1312: 1311: 1305: 1303: 1297: 1296: 1295: 1291: 1287: 1286:Deacon Vorbis 1282: 1278: 1277: 1276: 1275: 1271: 1267: 1266:Michael Hardy 1260: 1259: 1258: 1256: 1248: 1240: 1235: 1230: 1229: 1215: 1214: 1208: 1204: 1200: 1196: 1192: 1188: 1184: 1180: 1176: 1172: 1168: 1164: 1160: 1159: 1155: 1153: 1149: 1145: 1141: 1137: 1133: 1129: 1125: 1121: 1117: 1113: 1109: 1105: 1104: 1100: 1099: 1094: 1090: 1086: 1082: 1078: 1074: 1070: 1066: 1062: 1058: 1054: 1050: 1046: 1045: 1041: 1039: 1035: 1031: 1027: 1023: 1019: 1015: 1011: 1007: 1003: 999: 995: 991: 990: 986: 984: 980: 976: 972: 968: 964: 960: 956: 952: 948: 944: 940: 936: 935: 931: 929: 925: 921: 917: 913: 909: 905: 901: 897: 893: 889: 885: 881: 880: 876: 874: 870: 866: 862: 858: 854: 850: 846: 842: 838: 834: 830: 826: 825: 821: 819: 815: 811: 807: 803: 799: 795: 791: 787: 783: 779: 775: 771: 770: 766: 764: 760: 756: 752: 748: 744: 740: 736: 732: 728: 724: 720: 716: 715: 711: 709: 705: 701: 697: 693: 689: 685: 681: 677: 673: 669: 665: 661: 660: 656: 654: 650: 646: 642: 638: 634: 630: 626: 622: 618: 614: 610: 606: 605: 601: 599: 595: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 551: 550: 546: 544: 540: 536: 532: 528: 524: 520: 516: 512: 508: 504: 500: 496: 495: 491: 489: 485: 481: 477: 473: 469: 465: 461: 457: 453: 449: 445: 441: 440: 436: 434: 430: 426: 422: 418: 414: 410: 406: 402: 398: 394: 390: 386: 385: 381: 379: 375: 371: 367: 363: 359: 355: 351: 347: 343: 339: 335: 331: 330: 326: 324: 320: 316: 312: 308: 304: 300: 296: 292: 288: 284: 280: 276: 275: 271: 269: 265: 261: 257: 253: 249: 245: 241: 237: 233: 229: 225: 221: 220: 216: 214: 210: 206: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 165: 161: 159: 155: 151: 147: 143: 139: 135: 131: 127: 123: 119: 115: 111: 110: 106: 104: 100: 96: 92: 89: 85:Earlier years 81: 80: 77: 76: 72: 67: 62: 60: 55: 53: 48: 47: 41: 36: 35: 27: 23: 19: 6625: 6489: 6430: 6424: 6200: 6147: 6132: 6110: 6091: 6073: 6059: 6056:accordingly. 6050: 6016: 5991: 5986:User:Hesselp 5944: 5875: 5767: 5763: 5744: 5530: 5524: 5486: 5481: 5476: 5472: 5466: 5462: 5455: 5448: 5441: 5434: 5427: 5421: 5416: 5410: 5406: 5402: 5395: 5392: 5387: 5380: 5376: 5369: 5365: 5358: 5354: 5345: 5336: 5332: 5328: 5321: 5315: 5311: 5305: 5301: 5294: 5287: 5280: 5273: 5266: 5263:considered. 5260: 5256: 5245: 5238: 5231: 5224: 5217: 5216:an infinite 5211: 5204: 5203: 5186: 5184: 5179: 5175: 5169: 5165: 5158: 5151: 5144: 5137: 5130: 5124: 5120: 5115: 5111: 5108: 5102: 5099: 5095: 5089: 5086: 5080: 5077: 5071: 5067: 5061: 5055: 5051: 5047: 5040: 5034: 5030: 5024: 5020: 5013: 5006: 4999: 4992: 4985: 4982:considered. 4979: 4975: 4964: 4957: 4950: 4943: 4939: 4938:an infinite 4933: 4931: 4920: 4912: 4908: 4905: 4490: 4466: 4463:An infinite 4462: 4253: 4199: 4192: 4185: 4180: 4154: 4133: 4126: 4122: 4108: 4084: 4063: 4059: 4055: 4047: 4031: 4027: 4023: 4019: 3977: 3976:[or simply 3945: 3905: 3622: 3618: 3547: 3468: 3464: 3457: 3293: 3289: 3193: 3133:siddharthist 3056: 3013:This comment 2970:User:Hesselp 2968: 2958: 2952: 2946: 2940: 2934: 2928: 2913:User:Hesselp 2894: 2889: 2887: 2878: 2875:In geometry, 2874: 2872: 2863: 2861: 2729: 2714: 2687: 2681: 2653: 2627: 2593: 2531: 2511: 2505: 2483: 2454:132.209.3.30 2448: 2426:, including 2408: 2384:Hypersurface 2381: 2377:Hypersurface 2354: 2306: 2237: 2231: 2175: 2153: 2126:power~enwiki 2121: 2100: 2057: 1951: 1942: 1938: 1934: 1930: 1928: 1758: 1562: 1352:this section 1349: 1323: 1319: 1307: 1301: 1280: 1263: 1253:Opinions of 1252: 1233: 1156: 1101: 1042: 987: 932: 877: 822: 813: 767: 712: 657: 602: 547: 492: 437: 382: 327: 272: 217: 162: 107: 103:Sep–Dec 2004 99:Jan–Aug 2004 44: 6521:Looking at 6435:Anachronist 6179:Mark viking 6117:User:R.e.b. 5992:Please see 5479:increases. 5320:If the sum 5182:increases. 5125:to converge 5039:If the sum 4617:By the way 4056:On appelle 4032:convergente 3978:the series 2879:In algebra, 2830:Flat module 2814:mathematics 2780:Flat module 2764:ring theory 2753:mathematics 2734:Mark viking 2730:Mathematics 2717:mathematics 2649:Paul August 2645:these edits 1326:lowercase. 6531:Salix alba 6496:polynomial 6452:XOR'easter 6411:XOR'easter 6356:XOR'easter 6304:XOR'easter 6300:Here's one 6287:XOR'easter 6219:XOR'easter 5752:"a series" 5337:convergent 5056:convergent 4940:succession 4138:Bourbaki's 4050:starts in 3201:Sometimes 3190:An opinion 2956:block user 2950:filter log 2674:<-: --> 2570:They seem 2558:XOR'easter 2313:Modularity 2307:Presently 2250:XOR'easter 2182:XOR'easter 1328:XOR'easter 91:Motivation 6373:1211.1036 6051:I reply: 6023:submitted 4352:When the 4227:anymore. 4028:converger 3908:sequence 3172:, say. — 2962:block log 2641:this edit 2604:Tetrabrot 2499:nominated 2444:Tetrabrot 2430:violation 2124:of work. 1255:this edit 6649:Category 6579:D.Lazard 6561:between 6378:Headbomb 6349:at least 6322:Headbomb 6252:Headbomb 5926:D.Lazard 5551:D.Lazard 5461:+ ··· + 5300:+ ··· + 5218:sequence 5164:+ ··· + 5019:+ ··· + 4980:sequence 4934:sequence 4109:a series 2932:contribs 2826:topology 2818:geometry 2806:D.Lazard 2792:D.Lazard 2611:D.Lazard 2544:D.Lazard 2392:D.Lazard 2337:D.Lazard 24:‎ | 20:‎ | 6160:. Wow! 6045:Locales 6036:Schemes 5955:Hesselp 5884:Hesselp 5828:Hesselp 5776:Hesselp 5745:general 5655:Hesselp 5581:Hesselp 5491:Hesselp 5259:of the 5201:reads: 5187:without 4978:of the 4929:reads: 4472:Hesselp 4231:Hesselp 4205:+ ··· ( 4162:line 21 4083:That’s 3505:Hesselp 2921:Hesselp 2848:Quondum 2822:algebra 2706:Quondum 2578:Quondum 2487:Quondum 2469:Mathopo 2019:MathML 1234:15 days 22:Archive 6619:-: --> 6506:.) —- 6283:Reddit 5420:··· 5261:series 5251:, ... 5205:Series 5123:··· 4970:, ... 4923:1987, 4917:page 3 4736:where 4465:series 4254:series 4174:line 1 4064:series 3529::-) 3127:) and 3017:Tsirel 3000:Kmhkmh 2974:Series 2877:" or " 2678:loop. 2643:, and 2602:, and 2428:WP:3RR 2321:Module 2309:Module 2302:Module 2040:CiaPan 6369:arXiv 6352:twice 6279:blogs 6196:viXra 6021:" is 6017:Our " 5487:série 5265:Let 5257:terms 5212:série 5191:(see 4984:Let 4976:terms 4915:1973 4191:or 4105:19:54 4101:18:16 4058:série 3736:and 3619:three 3015:from 2915:again 2676:North 2540:WP:OR 2359:. —- 16:< 6636:talk 6632:Taku 6601:talk 6597:Taku 6583:talk 6549:talk 6545:Taku 6535:talk 6512:talk 6508:Taku 6462:talk 6440:talk 6415:talk 6360:talk 6308:talk 6291:talk 6281:and 6223:talk 6208:talk 6183:talk 6166:talk 6156:and 6152:for 6150:Ozob 6139:talk 6125:talk 6103:talk 6084:talk 6066:talk 6004:talk 5975:talk 5959:talk 5930:talk 5888:talk 5832:talk 5824:) ? 5780:talk 5709:talk 5659:talk 5620:talk 5585:talk 5555:talk 5545:and 5525:Reyk 5513:talk 5495:talk 5195:and 5098:··· 4890:talk 4886:Taku 4869:talk 4865:Taku 4787:and 4605:talk 4543:talk 4539:Taku 4476:talk 4437:talk 4433:Dmcq 4413:talk 4235:talk 4127:they 4123:They 4103:and 4085:your 3944:or 3684:, 3535:talk 3509:talk 3491:talk 3487:Dmcq 3475:talk 3178:talk 3174:Taku 3159:talk 3137:talk 3105:talk 3087:talk 3068:talk 3064:Taku 3044:talk 3025:talk 3004:talk 2988:talk 2944:logs 2926:talk 2903:talk 2838:talk 2796:talk 2786:and 2738:talk 2682:Reyk 2661:talk 2615:talk 2562:talk 2548:talk 2506:Reyk 2477:and 2396:talk 2365:talk 2361:Taku 2341:talk 2282:talk 2278:Taku 2268:talk 2264:Taku 2254:talk 2232:Reyk 2228:Ew. 2218:talk 2214:Taku 2200:talk 2196:Taku 2186:talk 2164:talk 2111:talk 2087:talk 2068:talk 2044:talk 1994:talk 1973:talk 1958:talk 1332:talk 1302:Reyk 1290:talk 1270:talk 1158:2024 1103:2023 1044:2022 989:2021 934:2020 879:2019 824:2018 769:2017 714:2016 659:2015 604:2014 549:2013 494:2012 439:2011 384:2010 329:2009 274:2008 219:2007 164:2006 109:2005 26:2017 6537:): 6498:or 6458:JBL 6431:JIR 6204:JBL 6025:to 5996:. 5754:". 5616:JBL 5532:YO! 5509:JBL 5475:as 5433:= 5391:··· 5346:sum 5272:= 5178:as 5068:for 5062:sum 4991:= 4229:-- 4209:). 4170:), 4164:), 4151:), 4142:EoM 4020:and 3628:). 3021:JBL 2820:or 2774:or 2715:In 2689:YO! 2647:). 2532:PhD 2513:YO! 2422:at 2319:to 2300:to 2239:YO! 2122:lot 2031:PNG 1904:sin 1895:cos 1883:cos 1874:sin 1846:sin 1833:sin 1824:sin 1812:cos 1803:cos 1775:cos 1724:cas 1706:cas 1685:cas 1670:cas 1652:cas 1634:cas 1616:cas 1601:cas 1577:cas 1529:cas 1510:cas 1488:cas 1472:cas 1453:cas 1434:cas 1415:cas 1399:cas 1374:cas 1354:of 1350:In 1309:YO! 1207:Dec 1203:Nov 1199:Oct 1195:Sep 1191:Aug 1187:Jul 1183:Jun 1179:May 1175:Apr 1171:Mar 1167:Feb 1163:Jan 1152:Dec 1148:Nov 1144:Oct 1140:Sep 1136:Aug 1132:Jul 1128:Jun 1124:May 1120:Apr 1116:Mar 1112:Feb 1108:Jan 1093:Dec 1089:Nov 1085:Oct 1081:Sep 1077:Aug 1073:Jul 1069:Jun 1065:May 1061:Apr 1057:Mar 1053:Feb 1049:Jan 1038:Dec 1034:Nov 1030:Oct 1026:Sep 1022:Aug 1018:Jul 1014:Jun 1010:May 1006:Apr 1002:Mar 998:Feb 994:Jan 983:Dec 979:Nov 975:Oct 971:Sep 967:Aug 963:Jul 959:Jun 955:May 951:Apr 947:Mar 943:Feb 939:Jan 928:Dec 924:Nov 920:Oct 916:Sep 912:Aug 908:Jul 904:Jun 900:May 896:Apr 892:Mar 888:Feb 884:Jan 873:Dec 869:Nov 865:Oct 861:Sep 857:Aug 853:Jul 849:Jun 845:May 841:Apr 837:Mar 833:Feb 829:Jan 818:Dec 814:Nov 810:Oct 806:Sep 802:Aug 798:Jul 794:Jun 790:May 786:Apr 782:Mar 778:Feb 774:Jan 763:Dec 759:Nov 755:Oct 751:Sep 747:Aug 743:Jul 739:Jun 735:May 731:Apr 727:Mar 723:Feb 719:Jan 708:Dec 704:Nov 700:Oct 696:Sep 692:Aug 688:Jul 684:Jun 680:May 676:Apr 672:Mar 668:Feb 664:Jan 653:Dec 649:Nov 645:Oct 641:Sep 637:Aug 633:Jul 629:Jun 625:May 621:Apr 617:Mar 613:Feb 609:Jan 598:Dec 594:Nov 590:Oct 586:Sep 582:Aug 578:Jul 574:Jun 570:May 566:Apr 562:Mar 558:Feb 554:Jan 543:Dec 539:Nov 535:Oct 531:Sep 527:Aug 523:Jul 519:Jun 515:May 511:Apr 507:Mar 503:Feb 499:Jan 488:Dec 484:Nov 480:Oct 476:Sep 472:Aug 468:Jul 464:Jun 460:May 456:Apr 452:Mar 448:Feb 444:Jan 433:Dec 429:Nov 425:Oct 421:Sep 417:Aug 413:Jul 409:Jun 405:May 401:Apr 397:Mar 393:Feb 389:Jan 378:Dec 374:Nov 370:Oct 366:Sep 362:Aug 358:Jul 354:Jun 350:May 346:Apr 342:Mar 338:Feb 334:Jan 323:Dec 319:Nov 315:Oct 311:Sep 307:Aug 303:Jul 299:Jun 295:May 291:Apr 287:Mar 283:Feb 279:Jan 268:Dec 264:Nov 260:Oct 256:Sep 252:Aug 248:Jul 244:Jun 240:May 236:Apr 232:Mar 228:Feb 224:Jan 213:Dec 209:Nov 205:Oct 201:Sep 197:Aug 193:Jul 189:Jun 185:May 181:Apr 177:Mar 173:Feb 169:Jan 158:Dec 154:Nov 150:Oct 146:Sep 142:Aug 138:Jul 134:Jun 130:May 126:Apr 122:Mar 118:Feb 114:Jan 6651:: 6638:) 6603:) 6585:) 6551:) 6514:) 6464:) 6417:) 6409:. 6392:· 6388:· 6384:· 6362:) 6354:. 6336:· 6332:· 6328:· 6310:) 6293:) 6266:· 6262:· 6258:· 6225:) 6210:) 6202:-- 6185:) 6168:) 6141:) 6127:) 6119:. 6115:, 6105:) 6097:. 6086:) 6078:. 6068:) 6006:) 5977:) 5961:) 5932:) 5924:. 5890:) 5834:) 5782:) 5770:? 5711:) 5661:) 5622:) 5614:-- 5587:) 5557:) 5515:) 5507:-- 5497:) 5469:-1 5454:+ 5447:+ 5440:+ 5424:, 5413:+1 5342:, 5308:-1 5293:+ 5286:+ 5279:+ 5244:, 5237:, 5230:, 5172:-1 5157:+ 5150:+ 5143:+ 5136:= 5127:, 5118:+1 5058:, 5027:-1 5012:+ 5005:+ 4998:+ 4963:, 4956:, 4949:, 4936:is 4932:A 4892:) 4871:) 4835:^ 4812:∙ 4803:π 4745:δ 4718:δ 4712:∞ 4707:∞ 4704:− 4700:∑ 4691:∙ 4682:π 4669:∞ 4664:∞ 4661:− 4657:∑ 4607:) 4574:∞ 4569:∞ 4566:− 4562:∑ 4545:) 4513:∞ 4508:∞ 4505:− 4501:∑ 4478:) 4439:) 4415:) 4407:-- 4325:∞ 4310:∑ 4303:⋯ 4237:) 4198:+ 4183:=1 4176:) 4144:. 4134:we 3874:∞ 3857:∑ 3819:. 3789:∞ 3772:∑ 3711:∞ 3694:∑ 3659:∞ 3590:∞ 3575:∑ 3537:) 3511:) 3493:) 3477:) 3226:∞ 3211:∑ 3180:) 3161:) 3153:. 3139:) 3131:. 3107:) 3089:) 3070:) 3046:) 3027:) 3006:) 2990:) 2905:) 2895:In 2840:) 2798:) 2740:) 2663:) 2617:) 2598:, 2564:) 2550:) 2497:I 2398:) 2367:) 2343:) 2335:. 2327:, 2284:) 2270:) 2256:) 2220:) 2202:) 2188:) 2180:? 2166:) 2140:) 2134:, 2113:) 2089:) 2070:) 2046:) 2038:-- 1996:) 1975:) 1960:) 1941:+ 1933:+ 1907:⁡ 1898:⁡ 1886:⁡ 1877:⁡ 1849:⁡ 1836:⁡ 1827:⁡ 1821:− 1815:⁡ 1806:⁡ 1778:⁡ 1733:− 1727:⁡ 1715:− 1709:⁡ 1703:− 1694:− 1688:⁡ 1673:⁡ 1655:⁡ 1643:− 1637:⁡ 1619:⁡ 1604:⁡ 1580:⁡ 1537:− 1518:− 1505:− 1496:− 1442:− 1334:) 1320:g, 1292:) 1272:) 1257:? 1205:· 1201:· 1197:· 1193:· 1189:· 1185:· 1181:· 1177:· 1173:· 1169:· 1165:· 1161:: 1150:· 1146:· 1142:· 1138:· 1134:· 1130:· 1126:· 1122:· 1118:· 1114:· 1110:· 1106:: 1091:· 1087:· 1083:· 1079:· 1075:· 1071:· 1067:· 1063:· 1059:· 1055:· 1051:· 1047:: 1036:· 1032:· 1028:· 1024:· 1020:· 1016:· 1012:· 1008:· 1004:· 1000:· 996:· 992:: 981:· 977:· 973:· 969:· 965:· 961:· 957:· 953:· 949:· 945:· 941:· 937:: 926:· 922:· 918:· 914:· 910:· 906:· 902:· 898:· 894:· 890:· 886:· 882:: 871:· 867:· 863:· 859:· 855:· 851:· 847:· 843:· 839:· 835:· 831:· 827:: 816:· 812:· 808:· 804:· 800:· 796:· 792:· 788:· 784:· 780:· 776:· 772:: 761:· 757:· 753:· 749:· 745:· 741:· 737:· 733:· 729:· 725:· 721:· 717:: 706:· 702:· 698:· 694:· 690:· 686:· 682:· 678:· 674:· 670:· 666:· 662:: 651:· 647:· 643:· 639:· 635:· 631:· 627:· 623:· 619:· 615:· 611:· 607:: 596:· 592:· 588:· 584:· 580:· 576:· 572:· 568:· 564:· 560:· 556:· 552:: 541:· 537:· 533:· 529:· 525:· 521:· 517:· 513:· 509:· 505:· 501:· 497:: 486:· 482:· 478:· 474:· 470:· 466:· 462:· 458:· 454:· 450:· 446:· 442:: 431:· 427:· 423:· 419:· 415:· 411:· 407:· 403:· 399:· 395:· 391:· 387:: 376:· 372:· 368:· 364:· 360:· 356:· 352:· 348:· 344:· 340:· 336:· 332:: 321:· 317:· 313:· 309:· 305:· 301:· 297:· 293:· 289:· 285:· 281:· 277:: 266:· 262:· 258:· 254:· 250:· 246:· 242:· 238:· 234:· 230:· 226:· 222:: 211:· 207:· 203:· 199:· 195:· 191:· 187:· 183:· 179:· 175:· 171:· 167:: 156:· 152:· 148:· 144:· 140:· 136:· 132:· 128:· 124:· 120:· 116:· 112:: 101:· 97:· 93:· 6634:( 6599:( 6581:( 6547:( 6533:( 6510:( 6460:( 6454:: 6450:@ 6442:) 6438:( 6413:( 6396:} 6394:b 6390:p 6386:c 6382:t 6380:{ 6371:: 6358:( 6340:} 6338:b 6334:p 6330:c 6326:t 6324:{ 6306:( 6289:( 6270:} 6268:b 6264:p 6260:c 6256:t 6254:{ 6242:/ 6239:/ 6236:/ 6221:( 6206:( 6181:( 6164:( 6137:( 6123:( 6101:( 6082:( 6064:( 6002:( 5973:( 5957:( 5945:@ 5928:( 5886:( 5830:( 5778:( 5707:( 5657:( 5618:( 5583:( 5553:( 5511:( 5493:( 5477:n 5473:s 5467:n 5463:u 5459:3 5456:u 5452:2 5449:u 5445:1 5442:u 5438:0 5435:u 5430:n 5428:s 5417:, 5411:n 5407:u 5403:, 5398:n 5396:u 5393:, 5388:, 5384:2 5381:u 5377:, 5373:1 5370:u 5366:, 5362:0 5359:u 5333:n 5329:s 5324:n 5322:s 5316:n 5312:n 5306:n 5302:u 5298:3 5295:u 5291:2 5288:u 5284:1 5281:u 5277:0 5274:u 5269:n 5267:s 5249:3 5246:u 5242:2 5239:u 5235:1 5232:u 5228:0 5225:u 5214:) 5199:) 5180:n 5176:s 5170:n 5166:u 5162:3 5159:u 5155:2 5152:u 5148:1 5145:u 5141:0 5138:u 5133:n 5131:s 5121:+ 5116:n 5112:u 5109:+ 5105:n 5103:u 5100:+ 5096:+ 5093:2 5090:u 5087:+ 5084:1 5081:u 5078:+ 5075:0 5072:u 5052:n 5048:s 5043:n 5041:s 5035:n 5031:n 5025:n 5021:u 5017:3 5014:u 5010:2 5007:u 5003:1 5000:u 4996:0 4993:u 4988:n 4986:s 4968:3 4965:u 4961:2 4958:u 4954:1 4951:u 4947:0 4944:u 4927:) 4888:( 4867:( 4847:) 4844:n 4841:( 4832:f 4826:= 4823:] 4820:f 4817:[ 4809:n 4806:i 4800:2 4796:e 4775:) 4772:n 4769:( 4766:f 4763:= 4760:] 4757:f 4754:[ 4749:n 4722:n 4696:= 4688:n 4685:i 4679:2 4675:e 4630:n 4626:a 4603:( 4584:n 4580:a 4541:( 4523:n 4519:a 4474:( 4435:( 4411:( 4392:n 4388:a 4365:n 4361:a 4340:. 4335:n 4331:a 4320:1 4317:= 4314:n 4306:= 4300:+ 4295:3 4291:a 4287:+ 4282:2 4278:a 4274:+ 4269:1 4265:a 4233:( 4203:2 4200:a 4196:1 4193:a 4188:n 4186:a 4181:n 4157:i 4155:a 4000:) 3995:n 3991:a 3987:( 3960:n 3956:a 3930:) 3925:n 3921:a 3917:( 3890:) 3884:n 3880:a 3867:0 3864:= 3861:n 3853:; 3848:) 3843:n 3839:a 3835:( 3831:( 3805:) 3799:n 3795:a 3782:0 3779:= 3776:n 3768:; 3763:) 3758:n 3754:a 3750:( 3746:( 3721:n 3717:a 3704:0 3701:= 3698:n 3669:n 3665:a 3652:0 3649:= 3646:n 3632:S 3625:n 3623:a 3600:n 3596:a 3585:1 3582:= 3579:n 3533:( 3507:( 3489:( 3473:( 3441:) 3434:n 3430:) 3424:n 3420:s 3416:( 3413:, 3408:n 3404:) 3398:n 3394:a 3390:( 3385:( 3361:n 3357:) 3351:n 3347:s 3343:( 3321:n 3317:) 3311:n 3307:a 3303:( 3269:. 3264:n 3260:a 3236:n 3232:a 3221:1 3218:= 3215:n 3176:( 3157:( 3135:( 3103:( 3085:( 3066:( 3042:( 3023:( 3002:( 2986:( 2964:) 2959:· 2953:· 2947:· 2941:· 2935:· 2929:· 2924:( 2901:( 2893:" 2836:( 2794:( 2736:( 2659:( 2613:( 2560:( 2546:( 2485:— 2394:( 2363:( 2339:( 2280:( 2266:( 2252:( 2216:( 2198:( 2184:( 2176:p 2162:( 2137:ν 2131:π 2128:( 2109:( 2085:( 2066:( 2042:( 1992:( 1986:: 1982:@ 1971:( 1956:( 1943:b 1939:a 1935:b 1931:a 1910:b 1901:a 1892:+ 1889:b 1880:a 1871:= 1864:) 1861:b 1858:+ 1855:a 1852:( 1839:b 1830:a 1818:b 1809:a 1800:= 1793:) 1790:b 1787:+ 1784:a 1781:( 1742:. 1739:) 1736:b 1730:( 1721:) 1718:a 1712:( 1700:) 1697:b 1691:( 1682:) 1679:a 1676:( 1667:+ 1664:) 1661:b 1658:( 1649:) 1646:a 1640:( 1631:+ 1628:) 1625:b 1622:( 1613:) 1610:a 1607:( 1598:= 1595:) 1592:b 1589:+ 1586:a 1583:( 1574:2 1546:. 1543:) 1540:b 1534:( 1524:) 1521:a 1515:( 1502:) 1499:b 1493:( 1483:) 1480:a 1477:( 1467:+ 1464:) 1461:b 1458:( 1448:) 1445:a 1439:( 1429:+ 1426:) 1423:b 1420:( 1410:) 1407:a 1404:( 1394:= 1391:) 1388:b 1385:+ 1382:a 1379:( 1369:2 1330:( 1324:g 1288:( 1268:( 1242:. 71:) 65:e 58:t 51:v

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Knowledge

talk:WikiProject Mathematics/Archive/2017/Nov - Knowledge

Index