Knowledge talk:WikiProject Mathematics/Archive/2022/Jul

1576:

me that this number has geometric and arithmetic properties that otherwise I might be entirely unaware of. For a number like 177 it might not seem impressive, but over time one compounds properties of different numbers and one is able to make quick connections because one recognizes properties shared with other numbers. If you take these away, then you take away the possibility of making these connections. I've always appreciated and learned best when I am presented with a more universal structure of whatever I am learning. If it's too limited, then I get a perspective that is not true to the subject. Even if the notability of some points might be less than others, comparative analysis permits you to surmise a nuanced nature of the number that otherwise would be nearly impossible to feel. At the very least, every single page should explain whether a number is prime or not, since it is not evident immediately for numbers even above 20 for most people - and whether it has 2, 3 or x amount of prime factors matters, since this is the very basic elementary definition of a number. Without this, no one can really know if for example 101 is prime or not, even though those who are experienced mathematicians might recognize that it is. And let's be honest. There would not be a gargantuan amount of lesser-important sequences that we can tie with given numbers. There really, are a very few amount of such "bad examples" to include. I imagine that, say, some numbers above 30 have about an average of maybe 5 lesser important sequences and properties that could be included. Is it really destructive at all to include many of them if they're so minimal in count (they can take 1 single line - i.e. a simple list in one sentence)? This is why I think it's very silly to not include these properties - there won't be very many attributable minor properties to these larger numbers anyways (like parts of sequences, types of numbers, etc.). So why not include them to give a more holistic background of a number? It let's people know they are part of other large sets, which yes, it is important! Uniqueness and shared-properties are opposites, however they can be equal in power insofar as what they communicate.

2076:

important as mathematical properties (say, being odd) should be preferred over properties that are unimportant (say, being a 60-gonal number) and that properties for which the number is particularly salient, likely to be cited as an example of that property, should be preferred over properties where the number is just one among many. My choice of "first half dozen members of an OEIS-nice sequence" is idiosyncratic, and I don't expect everyone else to agree with that exact choice, but it meets those principles. It also has the advantage of being somewhat objective; if we were going by my own opinion of what's interesting, for instance, I'd get rid of a lot more of the decimal-based properties (like "digitally balanced number"), but I recognize that others may find those more interesting than I do, and that's reflected in the fact that many of them are OEIS-nice. But obviously, you seem to think that my standard is the wrong standard. So can you please articulate a clear standard for what to include instead, one that is actually tenable rather than making a big pile of all properties that can either be sourced or calculated? It would not work to have an RFC with only a vague question rather than a clean yes-or-no question of whether some particular standard is a good one. My suspicion is that a general RFC is going to attract a lot of the kind of editors who have contributed to content like

2960:. The statement of the theorem was on page 176 (the proof is on the pages immediately after it). The citation for the theorem is given as "pp. 175−178" and this page range includes some - but not all - of the definitions/notation that are needed to understand the theorem as stated in that reference. The definitions of some the terms and notation that the reference used were defined elsewhere in hard to find locations (in this case as far away as pp. 151 and 157). If I didn't include these 2 pages then I think it likely that it would have been difficult for another person to verify that the statement and definitions were copied correctly. Now although in this particular case I used two separate citations (because of how many definitions were needed), there are occasionally other situations where this is not necessary and it would make much more sense to just use a single citation e.g. such as "pp. 151, 157, 175-176". I wish I could give a better example but I can't think of a better one off the top of my head. But did that clarify my question? 3427:(even though those terms are extremely rare in the literature even 25 years after the proof). The Poincaré conjecture is by far the most famous theorem proven by Perelman (since the mid 2000s and into the future, I would expect any use of the generic "Perelman theorem" to mean this, with other "Perelman theorems" named something more specific; for example in the three examples that David Eppstein found, the theorems there are explicitly called “Perelman’s Rigidity Theorem”, “Perelman's No Local Collapsing Theorem” and "Perelman’s Theorem on Shrinking Breathers in Ricci Flow" when introduced; none of these is presented as "Perelman's Theorem" without qualification). In a brief search of the current literature, there are a bunch of uses of "Poincaré–Perelman theorem" and a few direct uses of "Perelman theorem" to mean this result, but it is still commonly called the "Poincaré conjecture" after the proof, out of historical inertia. – 1705:, as in "oh, let's please this little guy who doesn't know what he is saying;" and even worse, suggesting that I actually meant I would put thousands of minor points on a Knowledge article, without realizing that I meant to add only several minor points, and then further saying I am wrongheaded. Ah, that passive aggressive nonchalance and condescending talk that just makes me think I wasted my time. Oh well, keep scruffing your cruft away, David. My time is better spent than trying to even bother with someone who is quite selfish as you are with coming to an agreement. But because you're an administrator, and I can tell you won't stop being selfish with your edits when others have a different perspective, I'm just going to spend my time otherwise. I hope you open your eyes to how rude you really can be on this platform, regardless of how much you have contributed here. Ciao. 1591:

that it sparks a connection is untenable, and more than that, wrongheaded: the more unimportant properties we list, the less likely that a reader coming to the article will notice and learn about the important ones, because they will be overwhelmed with unimportant minutiae. As for Blum numbers: their main significance comes in choosing keys for the RSA cryptosystem, for which the two prime factors should be large and independently random. Combining smallness and being a Blum number subtracts from the meaningfulness of the combination, rather than adding. So that is not a sequence where I am inclined to give a little leeway and say that maybe 11th is still early enough to be interesting, as I did for Leyland numbers. —

1827:. So my internal intuition is to include minor examples not as fillers per se, but as giving at least some color to these 100s and 200s numbers that can be exceedingly bland. Now, I want to apologize because I usually try not to be so rude myself, usually I prefer to have a more civil conversation, and I become irritated when my edits are just blanketed with a negative tone - there are also more civil ways to express disagreement than by asking a rhetorical question that is afixed to an edit. If you think I do not enjoy contributing meaningful edits, see 1572:

it takes an extra 3 lines. This obsession with only highly distinguishable properties is absurd, and hurts the content of the page. A distinguishable property of say, polite numbers, or square-free numbers is precisely that they incorporate such a large universe of numbers - and I would like to know personally whether a property is unique or shared by many other numbers. That is my personal philosophy, and usually having a pool of data that is well organized and diverse tends to be of greater service than limiting it to only the most notable examples.

2916:, but which also applies to other articles written by you. The references are not targeted enough. Example: footnote 6 refers to "Narici & Beckenstein 2011, pp. 371–423.", and is refered to from about 7 places. Pages 371-423 is a huge range of pages, a whole chapter maybe? Each place that refers to something in that chapter should refer to a specific result on a specific page of that chapter, instead of forcing the interested reader to read the whole chapter to figure things out. 2326:-- to phrase the if/then carefully: I think that if someone adds a reasonably written sentence or two relating in this kind of totally direct way to the topic of another wikipage, then it is good/reasonable policy to leave it in. I don't consider it imperative to add such material, or that it should exclude against other content. (As I see it, my essential point is just that the suggested criteria does not let in an unmanageable mess of content, at least for numbers like 177) 2840:

textbook references on functional analysis. (At present, it seems Banach spaces are not even mentioned on the page.) Having said that, I personally like the nature of much of your contributions to this page and other similar ones. But I might suggest it is more appropriate somewhere like nlab, where it is still easily accessible to those who want it, but where wiki can have a space for (what I would call) writing more encyclopedia than knowledge database.

40: 2267:

individual numbers seem not so interesting. The whole 177 page (along with many others analogous) could be deleted altogether without any real mathematical loss to wiki. But taking as given that we are talking about 177, the right choice is to send the reader to other pages for which 177 has some relevance. I may have no idea why someone would single out "Hilbert numbers" for significance, and it is absolutely not something which

4017:.) I don’t read/speak Latin and know very little about this subject so I don’t feel I can meaningfully contribute about it. But it seems like a topic that belongs in Knowledge, and I am sure there is a significant amount of secondary literature in English for anyone willing to hunt for it. Anyone knowledgeable about mathematical history want to take a crack at writing at least a few paragraphs? Edit: perhaps at 1767:" fail the test of appearing early in a sequence the OEIS designates as "nice" (or interesting in any other way, like being related to a hard open problem). In the latter case, 177 is so late in the sequence it's not even in the part that the OEIS prints explicitly. The 60-gonal numbers are easy to calculate and don't seem to be among the polygonal numbers that have been written about; contrast, for example, 1495:

labeled as nice by OEIS, and the number having that property should be among the first half-dozen or so numbers with that property. The version of 177 that I cut it down to includes only properties meeting that criterion. The additional properties you have been adding do not. Therefore, they are cruft, as useless as stating on every biography on Knowledge that the subject is human, with a head and two eyes. —

2303:. I do think there is actually a usefulness justification for including the combinatorial enumeration properties that would be dropped by your criterion: if one has a collection of 177 things, and looks up 177 to find that there are also 177 of some other kind of thing (star polygons, say), one might get a hint that the first kind of thing is secretly the same kind of thing as the second. — 3441:(By the way, I don't think it's wrong to keep calling it the Poincaré conjecture, given that Poincaré did in fact conjecture it. The assertions that it "was" a conjecture and "is now" a theorem are, I think, just wrong; if it's a theorem now then it has always been a theorem, even before there were humans. The proof has always existed; the only thing that has changed is that we now 3236:, since it is no longer a conjecture. I think this is unambiguously a bad move, since it is still (despite its status) universally called Poincaré conjecture and never called Perelman theorem; the user has simply decided that it ought to now be known as Perelman theorem instead. I don't understand well the technology of reverting page moves, hopefully someone else here does? 2057:. For instance, given that a number page like 177 exists, I think it is totally irrelevant/uninteresting whether that number is early or late in an OEIS list. Also, I think it is universally accepted to include "trivial" information on wiki, and that the website is better for it. The question is which trivial information should be included or excluded. 2734:; for finding the definition of the topology of uniform convergence (the subject of the first section), one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before. So, for understanding the definition, one needs to be an expert of the subject, or to spend several hours of hard work. 1802:

fails to produce results. I'm trying to move on from trying to make sense of why others see notability where you/anyone would maybe not, and vice-versa, whether it's light notability, or even two minor points which together might bring some interest to a number that has such few highly notable examples (some of the examples you chose to include, as

2576: 3462:"helpfully" move the page there in the future. Titles to be redirected have a much looser standard than the text of articles: redirects are about helping people find what they are looking for, not telling them what terms are standard usage. If you think there will be some confusion about whether Perelman theorem should refer to 4123:(mainly about bijections and double counting). There is another type of counting argument that is not linked: proof of the existence of an A that is not B, by counting both kinds of objects and finding that there are more A's than B's. Is there a good name for this type of argument, or better an existing article on it? — 2974:

That sound ok in this case. But in general, if we don't refer to other concepts defined elsewhere in the book, I think it would be perfectly fine to just cite the page where the theorem in given. It's up to the interested reader to figure out where the proof is and where the definitions of any used

2444:

There's really very little to distinguish 178. If not for the history of quadratic form enumeration, we might better not have an article there at all. Only one of the other listed properties is OEIS-nice, and neither has its own article. Anyway, I think any reader likely to be misled by the claims in

2294:

I don't think there's any need to apologize; it was interesting. I think idoneal should definitely be listed (finite sets of mathematical importance are different from the infinite and dense ones). Your approach is not unreasonable, but I think more difficult to implement: it takes a lot of effort to

2075:

Given that there are 6433 OEIS sequences matching 177 (noted above), and others under dispute where 177 is too far along the list to even be mentioned at OEIS (e.g. odd numbers), we obviously cannot include them all. We need some standard. As a general principle, I think that properties that are more

2060:

It seems that the only relevant official wiki-rules (as linked above on this thread) are for whether such a number page should exist in the first place, and is not very well-suited for advising on page content itself. Maybe a RFC (on the issue of content of general number pages) would be the best way

2812:

was intended to be about the various topologies that are used in functional analysis, which necessarily involves concepts such equicontinuous sets, bounded subsets, the Mackey topology, the ε-topology, and so on. I would like the article to be less technical and would love to hear suggestions on how

2259:

However I believe that all of the above (in terms of basic content) is appropriate for inclusion, although I am sure some here will call it "crust". It is all very easy to absorb (with one or two more complicated things), easily citable to oeis, would take up only little space (couple of paragraphs)

1990:

I strongly agree that indiscriminate piles of trivia are terrible on wikipedia, but strongly disagree that this counts as such (to the extent that I almost wonder if we're looking at the same thing). The "graph" (?) of bluelinks has as little complexity as ever present on wikipedia (you just have to

1806:

pointed out, could be interpreted as having average, or even no real notability - though I think they are good examples) - i.e. 60-gonal is a geometric representation of 177 in which its arithmetic average of its divisors also happens be a representation of 60, here as an integer itself. I find that

1590:

Mathematics is infinite. There are infinitely many properties, and infinitely many held by any number like 177. Even if one only goes by properties in OEIS, a search finds 6433 OEIS sequences matching 177. That is far too many to list. Your philosophy that we should list everything on the off chance

1575:

This is basic research philosophy, and the best way to present information - giving a comprehensive, and dynamic list of properties, even if some seem less important, there is still plenty learned from the way numbers mix with other numbers. Knowing 177 is a Blum integer and a polygonal number tells

1571:

It's fine. No issue. I disagree, but agree to disagree - except for the point on the Monster I agree it's OR. To me, an 11th Blum integer is definitely noteworthy. In fact, I think any studied and well-defined detail is noteworthy as long as they can be incorporated in groupings if possible, even if

1548:

a "nice" sequence, but 177 is 11th on the list, and while this will inevitably come down to a judgment call, it's not unreasonable to say that's too far down the line to be noteworthy. (I tend to find position in an OEIS list as more meaningful than how many there are below 1000, since the former is

4282:

There's a reason danger here of a person thinking these lists are a general listing of mathematical textbooks, e.g., "Undergraduate texts in mathematics" rather than the series "Undergraduate Texts in Mathematics". Since there are also similarly named series by publishers other than Springer, e.g.,

2839:

The material is too specialized for the subject matter. So I think that the solution is to not give the most general formulation possible. For instance, the primary context could be the weak convergence of continuous linear maps between Banach spaces, as is the context for many of the most standard

1942:

which as we are all aware amounts to totally rudimentary/routine computation on the elementary-school level. On the other hand, I see now that you are correct that "digitally balanced number" misleadingly links to external website, and so I agree with you that that sentence could/should be removed.

1801:

If a disagreement happens here, I rather speak of it here than move it elsewhere if there is a need of perspective for others to see abject behavior present. Moving it to another space for these types of issues I'd do if they continue, to take the matter at hand more directly if normal conversation

1446:

under its 196,884 dimensional representation - if this is too OR then I am perfectly fine with not including it. It seems to me that David Eppstein just wants to remove "cruft" he doesn't like because, well, personally he doesn't like it. He removed plenty of other information like examples of .177

2095:

I see, perhaps you are right about RFC. Anyway, although I agree with OEIS that many of their nice sequences are actually nice, it seems that their deployment thereof is based on an informal poll of their mailing list (I may be wrong, I couldn't find clear info), so I don't think it's a good basis

2052:

I agree with you for usual sentences, except that it would be strange to read the sentence in question in the usual way one reads sentences, as it is effectively (and very clearly, no matter one's comprehension of the content) a list only in sentence format. (It would be ok to convert to a literal

1875:

seem just as randomly selected as any of radlrb's (and arguably even moreso). So I agree with radlrb's edits. From reading David Eppstein's replies here, it seems his main contention is that radlrb's properties fail to, in and of themselves, make 177 a notable number, and I agree with him on this.

1494:

property of 3290041, one that makes it notable. In many AfDs, I have repeatedly expressed a specific and quantifiable version of this formulation: that to be interesting, the property must either have its own article here (or be deserving of an article through multiple in-depth publications) or be

4212:

I don't really see a good place where the general argument "set B is contained in A, and strictly smaller in some sense (measure, cardinality, whatever), so A\B is not empty" is described, so perhaps better not to link it. For infinite sets (a typical application is that the algebraic numbers are

3283:

Much thanks, Trovatore! SilverMatsu, I believe there is absolutely nothing called Perelman theorem with any consistency. From google search "Perelman theorem" could be a classification of Ricci solitons, sometimes it is the existence of Ricci flow with surgery, in principle it could be either the

2890:

was precisely because there was no article discussing uniform convergence in the general (non-normed space) setting of TVSs, and this was also why I did not add (norm space)-specialized content like what you suggested (i.e. weak convergence of continuous linear maps between Banach spaces). Having

2274:

the criteria I suggest (properties with their own wiki-page) is almost certainly not practical for some very common numbers like 0, 1, 2, etc. But such wiki pages probably have to be written by a different standard anyway, being as they are at the intersection of many different things. In present

2255:

proposing the above text for inclusion on the page, it is just raw data for discussion.) These are (unless I miss a couple) the fourteen named properties which are satisfied from the linked list of 215 potential ones. I think that all of us present will agree that a couple of these "named" number

1452:

These values are not unimportant. They define some of the characteristics of the number 177. To take out these properties leaves this number less notable. I am seeking mediation, as I have needed to continue reverting misguided edits by David Eppstein. He alone is not one to choose what goes on a

2540:

Not a problem to record this somewhere, and the Willerding article is a good place to mention this. But it is certainly not a "mathematical property" of the number 178, hence does not belong in that article. And let's be realistic, I doubt that any reader interested in integral quadratic forms

2266:

it seems some users here are using the criteria "what properties make 177 an interesting number". I am not using this criteria, since I think no natural numbers except probably 0 & 1 are themselves interesting. I think there are some interesting sequences (primes, Ramsey theory, etc) but the

2080:

which mixes easy-to-calculate unsourced mathematical properties held by most numbers with a large disambiguation-page-like random selection of links to bus routes numbered 155 and the like. The result of such an RFC could well be that any attempt to clean up this sort of mess would then have the

1489:

and its requirement for "three unrelated interesting mathematical properties" or "obvious cultural significance". That notability guideline gives, for instance, the example of the number 9870123 as not notable. Yet, one can say many of the same things about it: it is odd, it is semiprime... the

4347:

Knowledge only allows disambiguators on article titles when there is some other article that they disambiguate against. It generally only allows disambiguation pages when there are at least three ambiguous meanings for the title. These things are based on syntax (the wording of the title), not

2930:

You're right that large page ranges is bad practice. I have experienced the same problem you have (embarrassingly, a couple times with my own citations, which is why I've been doing that less frequently recently). But as you say, I should (and will) start making the page ranges more targeted.

2317:

Just to clarify two things: (1) if I were writing the page myself (and I do not anticipate making any edits) I probably would not include the graph enumeration properties but as is I have no strong suggestion on if they should stay or go; (relatedly, 2) I consider my proposed criteria as more

1810:

The funny thing, is that, in fact, as math evolves and we learn more about large numbers, large numbers will have properties themselves that require relatively large numbers also to describe. So these numbers above 150 or so tend to have scant significant properties, and the ones that do have

2364:, the next one in the sequence. And here it's becoming downright ridiculous. One of the claims of fame for that number 178 is that someone in 1946 claimed that there were 178 equivalence classes of something, and later that number was found incorrect. Makes no sense to have this in there. 3461:

Adding redirects here seems easy and low-cost (low chance of causing confusion; does not make false implications; as just a redirect, does not give “undue weight” to some fringe/unestablished usage), while potentially helping some readers. If nothing else, it prevents people from trying to

1963:

piles of trivia. When an article is just a heap of factoids, it's darn near impossible to tell what is important — or, in this area, what mathematicians have agreed upon as important. The goal here is to build an encyclopedia, not the TV Tropes of math. The apparent concision of "it's a

1447:

guns. It makes very little sense. People who come here and read these pages are often times not mathematicians, so yes, including information of numbers being odd, composite, and even semiprime, are important tidbits of information that inform people not well acquainted with mathematics.

4330:

This seems like a bad idea. These are well-known book series, and nobody ever says "undergraduate texts in mathematics" when talking about anything other than the Springer books. You can easily come up with another title if you want to talk about generic undergraduate textbooks.

1868:(with exception of monster group sentence, although I personally happen to like it) is perfectly concise/readable and the properties seem to all have their own wikipage (and are well-cited). This is precisely what I as a wiki reader would hope for from a page like 3552:

I'm not at all a stickler for the rules on talk pages; I'm not objecting to you talking about what you find interesting. I just don't want it to get confused with what our articles should be called or what redirects/disambigs we should have and where they should

2260:

to write out well, and on a page which contains practically no other information anyway. I like the graph enumeration properties presently given but I think they are less appropriate. The monster group properties are original research and should not be present.

1626:

If we have an article on a natural number, then I think that that article should contain, near the top, its factorization into prime numbers. This is a property which is not dependent on an arbitrary choice of base. It is frequently needed and not obvious.

2005:

Having to click on a link every three or four words to make it through a sentence is, I submit, not a good use of the hypertext medium. If a property is trivial, why write about it? The only justification I can think of is if the number is an oft-cited

1471:, these sequences are in OEIS and have proper identifying names, and 177 is in their lists early on. Also, I tried to find middle ground and removed two properties, however it seems to not be enough for him, he wants to appropriate the page entirely. 2096:

for anything here. And as I said before I also don't think that numbers towards the beginning of a sequence are more noteworthy. Anyway, my immediate thought is that it's reasonable to include named properties which have their own wikipage. Using

3781:

You might pick one of these articles and start a discussion on the talk page, then put a link on all of the other talk pages directed at that one, to see if anyone has a preference between σ vs. "sigma" in the title or minds unifying the titles.

1807:

interesting personally, especially since they arise from different operations. Take the example that 177 being a Leonardo number is 11th in its sequence (after two 1s), while the Blum example I wanted to include is also the 11th on its sequence.

3284:

geometrization conjecture or the Poincaré conjecture, and (by same principle) could be many other major results from his papers besides. I think there should not be any redirect or disambiguation page for "Perelman theorem."

4352:). So, in order to move these series names to disambigated titles, we need something else that would also be titled with the same exact wording and capitalization. What is that something else that you are thinking of? — 4457:

I simply redirected it, as there is no information for merging. Most of the Exterior article was taken from the Interior one in 2009, and the bulk of the remainder was added to both articles in 2021 in parallel edits.

1861:

Well, for what it's worth, I largely agree with Radlrb that David Eppstein can be rather condescending and rude in disagreement, sometimes not very nice to interact with as a fellow editor and especially not as an

4150:

It is related but I think not the same. The pigeonhole principle is about proving that functions from A to B are non-injective; here I'm more interested in proving that functions from B to A are non-surjective.

1543:

sum of prime factors is important; that would have to be established and documented independently. So, it's very hard to see a case for why we should include that property. As for the others: OEIS does call the

1912:

Not any kind of personal attack, my action is only to support other editors having similar difficulties to what I have had in the past. For what it's worth, I think you make a lot of valuable edits to the

4348:

semantics (the meaning of the title). Knowledge rules also generally allow different articles to have titles that differ only in capitalization, as long as they have hatnotes pointing to each other (see

3445:

a proof. Being a conjecture is more temporal; it's not a conjecture until someone conjectures it. Still, I don't think it stops being a conjecture just because we now know that it's also a theorem.

63: 2899:, etc. be mentioned early in the article (maybe the introduction) to help readers who are only interested in these special cases (and not the more general case) navigate to their desired article. 2764:"the topology of uniform convergence is defined for a much larger class of functions than the linear maps." Yes, there should be an article about this topic. I suggest that someone (not me) change " 1720:

If others are interested in keeping the point on 177 as a Blum integer, feel free to edit it back if David removes it, and if you think it's notable enough. Else, I think this case is closed.

2517: 2271:

177 interesting (I defer to previous few sentences), but wiki has singled it out so I think it is appropriate to send reader to "Hilbert number" page, despite my own distaste for the concept.

1796: 3488:"The Poincaré conjecture is by far the most famous theorem proven by Perelman". That does not preclude a disambiguation page. That can be the bolded primary meaning (cf the treatment at 2634: 3204: 2439: 1661: 2047: 1985: 3299: 3131:

Thank you. As a short-term fix, this does seem to work although it probably makes sense that there is a standalone article or a section in the elliptic curve article on this topic. —-

3055:, but as far as I can tell, that target has no info on the endomorphisms of elliptic curves (so the redirecting is unhelpful at best and misleading at worst). Is the topic not covered 4429:

Not deleted, but redirected. Yes, given the article contents, that seems reasonable (and if someone later finds more to write about exteriors, they can expand it out again later). --

3031:

Some verifiable explanation or definition of what constitutes an "Area of mathematics" would be useful if such exists. This appears to be the main subject of contention. Cheers · · ·

2545:. Any reader interested in that topic would access detailed references to this topic from other articles. No need to clutter these number articles with more non-mathematical facts. 2360:

seems to be an accumulation of random (trivial?) facts about that number, which may not all be notable enough to be in this encyclopedia. But just for comparison, I wandered over to

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This is not the same situation at all. We are talking about whether a certain statement is a "mathematical fact" that belongs in one on the "number articles". Not other contexts.

3981:

I was surprised that I couldn’t find any article concerning the use of Latin for writing European mathematics. From what I can tell the word “mathematics” does not occur in any of

2498: 1297:

Because Kodaira embedding theorem is one of the Fields commendation errors? I don't see any necessity to withdraw, I don't think either discussion has much effect on the other.

1253:

Since I saw today that the Fields Medals will be awarded next week, I was reminded of an issue I brought up here earlier this year, without resolution. I've opened a RFC at the

2236: 1157: 1102: 1043: 988: 933: 878: 823: 768: 713: 658: 603: 548: 493: 438: 383: 328: 273: 218: 163: 108: 25: 1843:(if I may refer to you with your first name). And maybe I am a little bland on some of these properties, however I try to provide good improvements. That is always my goal. 4194:

seems closer in spirit (and would work for the P/poly example, at least). My feeling is that such a link would be baffling, because you have to pore very carefully through

2167: 2032: 2622: 2588: 1467:

I'd like to also add that he does not have a proper definition of that "cruft" entails, he seems to be the only person in all of Knowledge enamoured with that phrase. Per

56: 2753:"one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before." I moved the section. Problem solved. 102: 98: 94: 90: 3950: 3824:

My impression from glancing at some books is that "Sigma" is more likely to be used in titles and headings, "σ" in the body of texts. Am I correct about such usage?

1612:

Sure. I rather choose to incorporate some minor points. Gladly you changed your mind on two properties you originally were against including. That's a win-win IMO.

4486: 2053:

bulleted list, but in my opinion it would not be an improvement.) Anyway, it seems we fundamentally have different criteria for what should go on a wikipage like

21: 2445:

the literature on the number of forms, and in need of correction, is more likely to find that correction at the 178 article than at the article on Willerding. —

49: 2295:

go through all of our number property articles (not all of which are listed on that template) and figure out which ones apply. You did miss some: it is also a

1976:..." is an illusion; parsing it requires traversing the graph of bluelinks, and sifting the properties that are trivially verifiable from those that are not. 4069:

and the ones right after it. The typesetting in many many many places in the article is wrong by the standards of ] and of standard typesetting conventions.

1991:

click on one thing to have the concept explained). I think it would be fine and good to rephrase to clarify which properties are trivial and which are not.

1701:

Ah, I read David's's last response wrong, I was busy working. Well, it doesn't matter, given that he thinks he owns these articles himself, per how he says

1652:, which seems a reasonable place for it, though of course of a factorization has a further interesting property then we can expound upon that in the prose. 3401:

So it definitely seems incorrect to redirect to Poincaré conjecture. If we had enough links for these other things we could consider making a dab page. —

3192: 1839:

which I am trying to slowly bring to good article standing. I love editing here, and I love making these pages better. And I do actually appreciate you

4374:

I was thinking that I would start new articles at the previous titles with a more general scope. But maybe you two are right. Perhaps it's a bad idea.

2655: 2554: 2531: 2454: 2070: 2000: 1693: 1679: 1585: 2099:

as a basis, here's where that would leave us for 177: (and just for fun, I have roughly ordered by how interesting I personally find each property)

3955:

Thanks! I made a go at stripping out unnecessary technicality (after all, the property in question doesn't depend on how one chooses to represent

3688: 3654: 1898:

violation, I do not find your assertions that "the properties seem to all have their own wikipage (and are well-cited)" particularly convincing. —

3810:

I think he means, not merger nor any content change in the articles, but to change the titles to either (1) all use "σ" or (2) all use "sigma".

2246:, which seems particularly interesting as a (to my non-expert eyes) natural number-theoretic condition with only 65, 66, or 67 of them existing. 1438:

in 24 dimensions. Aliquot sums and sums of divisors are common properties of numbers, and 196,883 is a particularly important number within the

4014: 3045: 17: 4291:

between our goal to be concise with titles and quickly get readers to the best article and our goals to be neutral and clear and unambiguous.

2378:

Suggestion to add for notability of the number 4: it's equal to the sum of the number of eyes and the number of ears of most vertebrates. :-)

3968: 3151:

I do not know enough about the topic to create a short description for the redirect. Maybe someone from the project could take a look. · · ·

3013: 2931:

However, I sometimes include the proof or relevant definitions/author comments in a citation's page range. Is that considered bad practice?.

1206: 1202: 1198: 4088:, instead of manually inserting HTML "&nbsp ;" around each side of the plus sign, wouldn't be easier to just let Latex do the job with 3763:

As for the direction of redirects, I don't care too much; either direction is ok (, and unification is nice to have, but not necessary). -

4183: 2913: 2887: 2809: 2788: 2780: 2723: 2703: 1523:"they are cruft, as useless as stating on every biography on Knowledge that the subject is human, with a head and two eyes." Well said! 3245: 4268: 4249: 4245: 4213:

countable, but the reals are uncountable, hence there exist transcendental numbers), this isn't covered by the pigeonhole principle. —

3590: 2584: 2568: 2787:

for arbitrary classes of functions. If an article on this topic is created then we could link to it and simplify the presentation in

1426:

I added 177 as the sum of the three prime factors (41, 59, 71) whose product make the minimum faithful complex representation of the

3225: 2957: 1890:

This is not the correct forum for making drive-by personal attacks. Perhaps a better forum, if that's what you want to do, would be

4302: 3393:...that positively curved ancient solutions have vanishing asymptotic volume ratio and infinite asymptotic scalar curvature ratio ( 2854:

The Banach space cases should be mentioned. However, there are already multiple articles dedicated to such topologies. The article

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The fact that it's the most famous theorem he's proved (so far) doesn't make it the primary meaning for "Perelman's theorem". --

3005: 2975:

concepts are in that source. No need to do it for them. The interested reader will learn more by looking things up themselves.

2879: 4309: 4298: 4284: 3365:...that the metric projection of a non-negatively curved open manifold onto its soul is a well-defined Riemannian submersion ( 3074: 1486: 1468: 3148:, When you create a redirect that you think should be expanded into an article, you can tag it with {{R with possibilities}} 1317:"Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to 4287:

series, it also seems biased to me to have Springer capitalize on such general phrases. There a bit of tension here in our

2891:

said that, this omission should be corrected as these cases are very important. I also suggest that links to articles like

2720:

As far as I know, the topology of uniform convergence is defined for a much larger class of functions than the linear maps.

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I have been working to remove huge piles of cruft that have been added over the years to many of our number articles (

1238: 3439:

OK, if/when that happens, we can make those redirects. Knowledge is not supposed to drive adoption of terminology.

2110:, i.e. it arises as the worst-case number of iterations needed for certain non-optimal sorting algorithms; it is an 3768: 3703: 1670:

To XOR'easter: Thanks for pointing that out. I am afraid that I have gotten into the habit of ignoring infoboxes.

1539:

Just because other sums of prime factors are important when it comes to the Monster group, it doesn't follow that

3748: 3467: 3266: 2618: 2580: 1894:. Also, given that the version you linked has an entire unsourced paragraph, multiple unlinked properties, and a 1684:

That's true, I also forget to look at infoboxes. Thank you for reminding me as well. Looks like we're set there.

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It really doesn't make any difference at all, for our current purposes, whether "Perelman's theorem" would be a

2010:

of having a property. (It is commonplace for natural numbers to have irrational square roots, but the fact that

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If by "unified" you mean all of them should be merged into just one article, that seems like a very bad idea.

3696:

The naming is merely a matter of directions of redirects. In your above order, the following redirects exist

2118:, meaning that it comes up in certain recursions (the latter being small modification of Fibonacci); it is a 1399:. I am copy-pasting the non-junk David Eppstein does not understand to include. He reverted my edits 4 times. 4074: 3829: 3800: 3498: 3489: 1646: 4001:, and these articles have little if any discussion of the use of Latin for science in general. The article 4002: 3682: 3648: 3586: 3578: 3463: 3424: 3329: 3229: 3168: 3136: 3112: 3108: 3090: 3078: 3064: 2863: 4379: 4320: 4182:

So you think it would be enlightening to readers to link the phrase "counting argument" as occurring in

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I may get around to fixing this eventually, but perhaps someone else would like to get there first: in

3325: 2462: 4195: 4191: 4165: 4116: 4038:. In that discussion, the most recent mathematics paper I could find written in Latin was from 2006 ( 3994: 3872: 3736: 2875: 2591:

until a consensus is reached, and readers of this page are welcome to contribute to the discussion.

2182: 1919: 1820: 2195: 4448: 4434: 4419: 4411: 4407: 4403: 4399: 4353: 4339: 4199: 4152: 4142: 4124: 4120: 4097: 4046: 4025: 3964: 3927: 3815: 3786: 3727: 3672: 3641: 3582: 3560: 3513: 3478: 3452: 3431: 3402: 3353: 3340: 3321: 3256: 3233: 2980: 2947: 2921: 2892: 2855: 2805: 2784: 2768:" from a redirect into an article about this topic. Or maybe change it into a disambiguation page. 2765: 2731: 2707: 2699: 2686: 2550: 2527: 2446: 2419: 2405: 2397: 2383: 2369: 2304: 2300: 2082: 1899: 1840: 1746: 1675: 1632: 1592: 1528: 1496: 1439: 1381: 1380:) has been edit-warring to add back the cruft. I've reached the limit of my reverts. Help wanted. — 1318: 3667:

is a concept from topology and should be kept separate from the other topics from measure theory.

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The issue can be a subtle one: The most precise explanation is to say that although the complex

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These articles state clearly at the top what they are about. Doesn’t seem like a real danger. –

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is an article that should concern all of use. Its state is presently awful. I have started an

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I suggest we have the following properties for 177, since David Eppstein is warring my edits:

1396: 3524:

If we called Poincaré conjecture as Perelman's theorem, I think we miss the contributions of

3394: 3215: 2177:). Since both prime factors are of the form 4n+3, it is the special kind of semiprime called 4375: 4316: 3998: 3942: 3598: 3533: 3529: 3471: 3416: 3383: 3376: 3333: 3303: 3270: 3251:

Thanks for flagging this. I have reverted. Presumably bots will clean up the redirects. --

3196: 3152: 3032: 2647: 2641: 2626: 2600: 2592: 2509: 2505: 2431: 2296: 2097: 2039: 1977: 1922: 1848: 1824: 1788: 1760: 1725: 1710: 1689: 1653: 1617: 1581: 1558: 1514: 1476: 1458: 1420: 1371: 1332: 1322: 1284: 1221: 1219: 39: 4042: 3382:...that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons ( 3373: 1434:

has a faithful representation under 96,256 dimensions, whose sum of digits is 196,560, the

4218: 4173: 4039: 4006: 3853: 2115: 1735: 3707: 2280:

Apologies for the long message, I try to stay concise but it does not come natural to me

1485:

In fact, I do have a definition of "cruft": it is anything that would not be relevant to

2942:

Not sure I understand what the last sentence is referring to. Can you give an example?

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is so technical is because there is no article dedicated to the more general theory of

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case, and for similar numbers, I think it leads to a reasonable amount of information.

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types are totally uninteresting and perhaps should not even have their own wiki page!

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And yet, despite claiming that you consider the matter closed, and resorting here to

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There's a reason danger here of a person thinking these lists are a general listing.

3941:

for that definition is actually to Bourbaki, which may be pedagogically suboptimal.

3163:

Thank you for letting me know about the tag. I have added the short description. —-

3990: 3893: 3740: 3681:

I'm talking about the naming of the articles; not sure how your point is relevant.

3117: 3082: 2971: 2961: 2932: 2900: 2829: 2825: 2814: 2792: 2769: 2754: 2727: 2542: 2427: 2415: 2393: 2361: 2357: 2178: 2174: 2054: 1895: 1869: 1836: 1812: 1545: 1453:

page, or not; and neither am I. So if we can get proper input that would be great.

1431: 1406: 1363: 1352: 1312: 1280: 1254: 3631: 2356:

I would tend to have the same opinion as David Eppstein in this matter. The page

2130:, meaning that it and its prime factorization have the same total number of digits 1557:

includes that property, so maybe we don't have a substantial disagreement there.

4279:

names the "main" redirect" (with article possibility) or a disambiguation page.

4084:

Your changes are an improvement. But as an example, when changing the original

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I suggest delete the Perelman theorem, because, as another example, I think the

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talk page to do with erroneous commendations, please feel free to comment there

2706:. Moreover, the topology of uniform convergence is not explicitly mentioned in 1430:. This is not trivial, it is another set value of these digits. I.e. the group 4214: 4169: 3712: 3626: 3387: 3051:

The link in the title (as you can see) is red. I thought of redirecting it to

3907:

which keep each real number fixed: The identity and the automorphism sending

2034:

is irrational has been much remarked upon.) This is what the "does it appear

2589:

Knowledge:Redirects for discussion/Log/2022 July 1#Kodaira embedding theorem

2170: 1925: 3717: 2886:. If I remember correctly, the reason why I originally created the article 3922:(It would also be nice if this statement were supported by a citation.) -- 1283:. Should I withdraw this once and wait a while before re-nominated it? -- 2730:. This article is awfully written: almost no context provided; much too 2575: 2185:, so that it is not the hypotenuse of any integer-sided right triangle. 3362:

Searching Google scholar for "Perelman's theorem" finds it continued:

3348:

Is there evidence that these phrases are used in the wild for that? --

2426:

covers failed proofs, i.e., "facts" about maps that turned out wrong;

4187: 1811:

significant properties tend to come in sets, like for say the number

2414:

Recording the history of such things seems to make as much sense in

2392:

I have moved the information about the incorrect number of ... from

1872:. The four mathematical facts in David Eppstein's preferred version 2137:, so that the average of its divisors (1, 3, 59, 177) is an integer 1311:

Thank you your reply. I'm worried about breaking the wiki-link in

3875: 1916:

Anyway, the "entire unsourced paragraph" you refer to seems to be

1876:

But I think it is a bad standard to use for the question at hand.

4005:

doesn’t really describe this in any detail. (There is an article

3959:), so it's now a bit blander but perhaps more comprehensible. -- 2623:

Knowledge:Redirects_for_discussion/Log/2022_July_1#Hodge_manifold

2541:

would get their first information on that topic from the article

2106:, i.e. the binary expansion has an even number of ones; it is a 3014:

Talk:Glossary of areas of mathematics#RfC on inclusion criteria

2579:

An editor has identified a potential problem with the redirect

2459:

An analogy that just sprang to mind is that we wouldn't remove

1224: 33: 4138:

Isn’t this just an application of the pigeonhole principle? –

3585:

is inappropriate, a disambiguation page with links to, e.g.,

1865:

Anyway, as for the matter itself, radlrb's preferred version

4115:, a disambiguation page, currently links to two topics: the 1772: 1768: 2958:

Complete topological vector space#Topology of a completion

2779:

Side note: I think that part of the reason by the article

1943:

I'm not sure what other unlinked properties you refer to.

4312:

becoming the "main" redirect (with article possibility).

1929: 3472:

Grigori Perelman#Geometrization and Poincaré conjectures

3334:

Grigori Perelman#Geometrization and Poincaré conjectures

4066: 3113:

Complex multiplication#Abstract theory of endomorphisms

2694: 2681: 2669: 2242:

since all groups of order 177 are cyclic. And it is an

2077: 1873: 1866: 1742: 1554: 1359: 3081:

but not the general one with the product given by the

3012:

on inclusions criterias for this stand-alone list, at

4264:

to disambiguate them and then make the uncapitalized

3210:

Move of "Poincaré conjecture" to "Perelman's theorem"

2956:

Consider "Grothendieck's Completeness Theorem" here:

2465: 2430:

can record a "fact" about 178 that turned out wrong.

2198: 2146: 2016: 1490:

conclusion is that being odd and semiprime is not an

1315:

because RfD temporarily broke the redirect (example:

1741:

rather than content-based discussion, you are still

2492: 2230: 2161: 2126:, meaning that it is not a power of two; it is an 2026: 3550:name. We shouldn't even be talking about that. 3059:in Knowledge (if so, that's very surprising.) -- 2038:in the OEIS list?" question is trying to get at. 1815:, which is a geometrically important number (in E 4250:Undergraduate Texts in Mathematics (book series) 4184:Garden of Eden (cellular automaton)#Proof sketch 3077:also doesn't exist either (a special case is in 1959:One thing I don't like as a Knowledge reader is 4402:has nearly identical contents with the section 2856:Operator topologies#List of topologies on B(H) 4303:Graduate Studies in Mathematics (book series) 4166:Pigeonhole_principle#Alternative_formulations 3850:, one finds the amazing three-colon sentence 2122:, meaning that it is of the form 4n+1; it is 1232:This page has archives. Sections older than 57: 8: 4241:I think we should rename these two articles 4259:Graduate Texts in Mathematics (book series) 4237:Moving Spinger series articles to new names 1549:about the sequence itself.) 177 is the 8th 3195:may be of interest to the community here. 64: 50: 2726:is an article almost entirely written by 2480: 2475: 2470: 2464: 2222: 2209: 2197: 2145: 2017: 2015: 1823:for example) as well as a number that is 1779:, or the depth of coverage available for 1395:Yes, please help. See my comments on the 3595:Shmuel (Seymour J.) Metz Username:Chatul 4011:Lingua franca#Historical lingua francas 3001:RfC on Glossary of areas of mathematics 2738:What should be done with these issues? 2621:and are being discussed in the section 2424:Four_color_theorem#Early_proof_attempts 88: 4332: 4015:Latin translations of the 12th century 3851: 3046:Endomorphism ring of an elliptic curve 2567:"Kodaira embedding theorem" listed at 1316: 18:Knowledge talk:WikiProject Mathematics 4487:WikiProject Mathematics archives/2022 4404:Interior (topology)#Exterior of a set 3761:I suggest to create the red redirect. 3269:are also known as Perelman theorem.-- 7: 4013:, and a somewhat related article at 4009:, and about 2 relevant sentences at 3647:Looks like these should be unified. 3377:Grigori Perelman#Comparison geometry 3107:The ideal target right now would be 1771:the OEIS has to say about them with 1743:adding more uninteresting properties 2914:Topologies on spaces of linear maps 2888:Topologies on spaces of linear maps 2810:Topologies on spaces of linear maps 2789:Topologies on spaces of linear maps 2781:Topologies on spaces of linear maps 2724:Topologies on spaces of linear maps 2704:Topologies on spaces of linear maps 1409:: 11th and less than 60 below 1000. 4269:Undergraduate texts in mathematics 4246:Undergraduate Texts in Mathematics 3591:Thurston geometrization conjecture 2673:redirects to an eponym section of 45:WikiProject Mathematics archives ( 32: 2670:Topology of pointwise convergence 2646:Thank you for fixing the link. -- 2493:{\displaystyle 10^{10^{10^{34}}}} 2081:weight of consensus against it. — 1423:as there are very few below 1000. 1416:as there are very few below 1000. 1236:may be automatically archived by 3474:should eliminate that concern. – 3085:with variable coefficients.) -- 3006:Glossary of areas of mathematics 2880:Weak convergence (Hilbert space) 2587:. This discussion will occur at 2574: 38: 4410:be merged into that section of 4310:Graduate studies in mathematics 4299:Graduate Studies in Mathematics 4285:Graduate Studies in Mathematics 3889:isomorphism: There are exactly 2858:lists many of them, including: 2695:Topology of uniform convergence 2682:Topology of compact convergence 2231:{\displaystyle 177=2^{7}+7^{2}} 3698:(blue) resp. don't exist (red) 3415:As a comparable example, both 3075:ring of differential operators 2396:, where it did not belong, to 1487:Knowledge:Notability (numbers) 1469:Knowledge:Notability (numbers) 1351:Editor adding junk content to 1: 4274:Graduate texts in mathematics 4255:Graduate Texts in Mathematics 4168:also mentions that version. — 3937:Impressive! The citation in 3577:While I agree that a move of 3209: 3016:. Contributions are welcome. 2717:Coherency of redirect targets 4198:to find the relevant part. — 3663:I don't think so. At least 2824:"almost entirely written by 2614:I believe the redirects are 2506:that bound has been improved 2240:cyclic number (group theory) 3977:Use of Latin in Mathematics 3617:Sigma-additive set function 2702:. Instead, it redirects to 2299:and (as discussed above) a 2181:. The same fact makes it a 2162:{\displaystyle 3\times 59,} 2140:Its prime factorization is 2027:{\displaystyle {\sqrt {2}}} 1759:I have to agree that both " 4503: 3593:, might be appropriate. -- 2713:This sets several issues: 1325:, that such varieties are 4468:08:27, 29 July 2022 (UTC) 4453:01:51, 29 July 2022 (UTC) 4443:Yes, I meant redirected. 4439:19:11, 28 July 2022 (UTC) 4424:01:22, 28 July 2022 (UTC) 4384:03:47, 28 July 2022 (UTC) 4362:03:36, 28 July 2022 (UTC) 4343:03:34, 28 July 2022 (UTC) 4325:03:13, 28 July 2022 (UTC) 4223:19:59, 24 July 2022 (UTC) 4208:19:04, 24 July 2022 (UTC) 4178:18:25, 24 July 2022 (UTC) 4161:18:09, 24 July 2022 (UTC) 4146:17:41, 24 July 2022 (UTC) 4133:01:05, 24 July 2022 (UTC) 4102:02:39, 24 July 2022 (UTC) 4079:00:41, 23 July 2022 (UTC) 4055:21:37, 23 July 2022 (UTC) 4029:21:25, 23 July 2022 (UTC) 3969:17:44, 23 July 2022 (UTC) 3951:22:21, 22 July 2022 (UTC) 3932:22:09, 22 July 2022 (UTC) 3834:15:05, 23 July 2022 (UTC) 3820:05:55, 23 July 2022 (UTC) 3805:00:16, 23 July 2022 (UTC) 3790:21:46, 21 July 2022 (UTC) 3773:11:14, 21 July 2022 (UTC) 3749:Sigma-algebra of tau-past 3692:10:46, 21 July 2022 (UTC) 3677:04:42, 21 July 2022 (UTC) 3658:20:49, 20 July 2022 (UTC) 3603:11:18, 12 July 2022 (UTC) 3565:15:48, 14 July 2022 (UTC) 3542:04:36, 14 July 2022 (UTC) 3518:17:51, 13 July 2022 (UTC) 3504:17:44, 13 July 2022 (UTC) 3482:21:02, 11 July 2022 (UTC) 3468:Geometrization conjecture 3457:20:49, 11 July 2022 (UTC) 3435:20:32, 11 July 2022 (UTC) 3411:20:25, 11 July 2022 (UTC) 3388:10.1007/s12220-017-9974-1 3358:19:32, 11 July 2022 (UTC) 3344:17:42, 11 July 2022 (UTC) 3312:16:37, 11 July 2022 (UTC) 3294:14:20, 10 July 2022 (UTC) 3279:04:16, 10 July 2022 (UTC) 3267:Geometrization conjecture 3261:03:52, 10 July 2022 (UTC) 3246:03:23, 10 July 2022 (UTC) 3205:14:26, 14 July 2022 (UTC) 3187:Łukaszyk–Karmowski metric 2906:19:50, 30 June 2022 (UTC) 2850:19:16, 30 June 2022 (UTC) 2835:18:00, 30 June 2022 (UTC) 2820:18:00, 30 June 2022 (UTC) 2798:18:12, 30 June 2022 (UTC) 2775:17:45, 30 June 2022 (UTC) 2760:17:45, 30 June 2022 (UTC) 2748:17:18, 30 June 2022 (UTC) 2619:Kodaira embedding theorem 2581:Kodaira embedding theorem 2336:06:13, 30 June 2022 (UTC) 2313:05:34, 30 June 2022 (UTC) 2290:04:41, 30 June 2022 (UTC) 2091:00:38, 30 June 2022 (UTC) 2071:23:59, 29 June 2022 (UTC) 2048:21:25, 29 June 2022 (UTC) 2001:21:17, 29 June 2022 (UTC) 1986:21:11, 29 June 2022 (UTC) 1953:21:09, 29 June 2022 (UTC) 1908:20:55, 29 June 2022 (UTC) 1886:20:23, 29 June 2022 (UTC) 1853:05:43, 30 June 2022 (UTC) 1797:19:56, 29 June 2022 (UTC) 1755:19:36, 29 June 2022 (UTC) 1730:07:48, 29 June 2022 (UTC) 1715:07:27, 29 June 2022 (UTC) 1694:00:00, 29 June 2022 (UTC) 1680:23:00, 28 June 2022 (UTC) 1662:22:56, 28 June 2022 (UTC) 1637:22:41, 28 June 2022 (UTC) 1622:22:34, 28 June 2022 (UTC) 1601:21:34, 28 June 2022 (UTC) 1586:21:20, 28 June 2022 (UTC) 1567:18:59, 28 June 2022 (UTC) 1533:23:56, 28 June 2022 (UTC) 1519:20:56, 28 June 2022 (UTC) 1505:18:51, 28 June 2022 (UTC) 1481:18:43, 28 June 2022 (UTC) 1463:18:24, 28 June 2022 (UTC) 1442:as it is linked with the 1390:18:15, 28 June 2022 (UTC) 1279:I started RfD related to 1267:20:24, 30 June 2022 (UTC) 4021:or some similar title. – 3173:13:21, 7 July 2022 (UTC) 3159:07:27, 6 July 2022 (UTC) 3141:08:23, 5 July 2022 (UTC) 3127:13:42, 4 July 2022 (UTC) 3095:08:38, 4 July 2022 (UTC) 3069:08:32, 4 July 2022 (UTC) 3039:07:10, 6 July 2022 (UTC) 3026:15:28, 5 July 2022 (UTC) 2985:04:35, 5 July 2022 (UTC) 2967:08:15, 2 July 2022 (UTC) 2952:23:30, 1 July 2022 (UTC) 2938:21:42, 1 July 2022 (UTC) 2926:04:30, 1 July 2022 (UTC) 2897:Strong operator topology 2860:Strong operator topology 2656:00:07, 2 July 2022 (UTC) 2635:16:08, 1 July 2022 (UTC) 2609:04:43, 1 July 2022 (UTC) 2569:Redirects for discussion 2555:23:25, 1 July 2022 (UTC) 2532:23:34, 1 July 2022 (UTC) 2518:22:53, 1 July 2022 (UTC) 2455:22:45, 1 July 2022 (UTC) 2440:22:42, 1 July 2022 (UTC) 2410:22:33, 1 July 2022 (UTC) 2388:04:11, 1 July 2022 (UTC) 2374:04:08, 1 July 2022 (UTC) 2078:the current state of 155 1781:square triangular number 1341:05:53, 1 July 2022 (UTC) 1307:05:19, 1 July 2022 (UTC) 1293:05:00, 1 July 2022 (UTC) 3704:σ-additive set function 3490:Rabbit (disambiguation) 3375:); this seems to match 2583:and has thus listed it 1553:, but David Eppstein's 4003:History of mathematics 3109:Complex multiplication 3079:differential operators 2864:Weak operator topology 2494: 2232: 2163: 2028: 1745:back to the article. — 1321:. He demonstrated, by 1239:Lowercase sigmabot III 4294:Similarly, I propose 3470:, then a redirect to 3425:Fermat's Last Theorem 3228:) has recently moved 2698:does not redirect to 2675:Pointwise convergence 2495: 2233: 2164: 2029: 4289:article title policy 4196:pigeonhole principle 4192:Probabilistic method 4117:pigeonhole principle 3995:Ecclesiastical Latin 3737:sigma-finite measure 2876:Ultrastrong topology 2813:to accomplish this. 2500:to the biography of 2463: 2263:Two extra thoughts: 2196: 2183:nonhypotenuse number 2144: 2014: 1821:icosahedral symmetry 1555:most recent revision 4412:Interior (topology) 4408:Exterior (topology) 4400:Exterior (topology) 4121:combinatorial proof 3894:field automorphisms 3753:σ-Algebra of τ-past 3728:sigma-compact space 3587:Poincaré conjecture 3579:Poincaré conjecture 3464:Poincaré conjecture 3330:Poincaré conjecture 3328:redirect to either 3230:Poincaré conjecture 3185:Deletion review of 2893:Operator topologies 2785:Uniform convergence 2766:Uniform convergence 2708:Uniform convergence 2700:Uniform convergence 2687:Compact convergence 2420:Margaret Willerding 2398:Margaret Willerding 2301:square-free integer 1440:monstrous moonshine 1319:algebraic varieties 1249:RFC at Fields Medal 4414:and then deleted? 4186:or in the lead of 4036:related discussion 4019:Mathematical Latin 3747:Moreover, I found 3583:Perelman's theorem 3322:Perelman's theorem 3234:Perelman's theorem 3073:Incidentally, the 2912:One comment about 2872:Ultraweak topology 2490: 2228: 2159: 2128:equidigital number 2024: 1970:square-free number 1785:cannonball problem 4394:Exterior of a set 4315:Thoughts? Ideas? 4113:Counting argument 4108:Counting argument 4091:n+2</math: --> 3987:Renaissance Latin 3554: 3446: 3122: 2135:arithmetic number 2022: 1777:hexagonal numbers 1765:arithmetic number 1397:Talk:177 (number) 1246: 1245: 95:Nov 2002–Dec 2003 4494: 4092: 4087: 3999:History of Latin 3919: 3912: 3906: 3866: 3765:Jochen Burghardt 3642:σ-finite measure 3551: 3530:Michael Freedman 3440: 3326:Perelman theorem 3125: 3120: 3106: 2964: 2935: 2903: 2832: 2817: 2795: 2772: 2757: 2697: 2684: 2672: 2645: 2578: 2499: 2497: 2496: 2491: 2489: 2488: 2487: 2486: 2485: 2484: 2297:deficient number 2237: 2235: 2234: 2229: 2227: 2226: 2214: 2213: 2168: 2166: 2165: 2160: 2033: 2031: 2030: 2025: 2023: 2018: 1825:highly composite 1739:personal attacks 1703:im giving leeway 1651: 1645: 1323:sheaf cohomology 1278: 1241: 1225: 66: 59: 52: 42: 34: 4502: 4501: 4497: 4496: 4495: 4493: 4492: 4491: 4477: 4476: 4396: 4239: 4110: 4089: 4085: 4063: 4061:Bad typesetting 4007:Botanical Latin 3979: 3914: 3908: 3897: 3885:unique up to a 3857: 3844: 3751:redirecting to 3665:σ-compact space 3637:σ-compact space 3613: 3417:Wiles's theorem 3212: 3193:This discussion 3190: 3153:Peter Southwood 3123: 3116: 3100: 3049: 3033:Peter Southwood 3003: 2962: 2933: 2901: 2830: 2815: 2793: 2770: 2755: 2693: 2680: 2668: 2666: 2664:Topology of ... 2639: 2572: 2476: 2471: 2466: 2461: 2460: 2218: 2205: 2194: 2193: 2169:which makes it 2142: 2141: 2116:Leonardo number 2012: 2011: 1818: 1761:60-gonal number 1649: 1643: 1642:That's done in 1421:60-gonal number 1356: 1327:Hodge manifolds 1272: 1251: 1237: 1226: 1220: 1211: 1097: 87: 86: 73: 70: 30: 29: 28: 12: 11: 5: 4500: 4498: 4490: 4489: 4479: 4478: 4475: 4474: 4473: 4472: 4471: 4470: 4395: 4392: 4391: 4390: 4389: 4388: 4387: 4386: 4367: 4366: 4365: 4364: 4354:David Eppstein 4306: 4305: 4277: 4276: 4271: 4262: 4261: 4252: 4238: 4235: 4234: 4233: 4232: 4231: 4230: 4229: 4228: 4227: 4226: 4225: 4200:David Eppstein 4153:David Eppstein 4125:David Eppstein 4109: 4106: 4105: 4104: 4062: 4059: 4058: 4057: 4047:David Eppstein 3983:Medieval Latin 3978: 3975: 3974: 3973: 3972: 3971: 3939:complex number 3869:complex number 3848:Imaginary unit 3843: 3840: 3839: 3838: 3837: 3836: 3793: 3792: 3779: 3778: 3777: 3776: 3775: 3755:(no idea what 3745: 3744: 3743: 3734: 3725: 3720: 3715: 3710: 3645: 3644: 3639: 3634: 3629: 3624: 3619: 3612: 3609: 3608: 3607: 3606: 3605: 3575: 3574: 3573: 3572: 3571: 3570: 3569: 3568: 3567: 3522: 3521: 3520: 3486: 3485: 3484: 3413: 3403:David Eppstein 3399: 3398: 3397: 3391: 3380: 3318: 3317: 3316: 3315: 3314: 3298:Nominated for 3211: 3208: 3189: 3183: 3182: 3181: 3180: 3179: 3178: 3177: 3176: 3175: 3149: 3119: 3053:elliptic curve 3048: 3043: 3042: 3041: 3002: 2999: 2998: 2997: 2996: 2995: 2994: 2993: 2992: 2991: 2990: 2989: 2988: 2987: 2910: 2909: 2908: 2822: 2808:" The article 2802: 2801: 2800: 2762: 2736: 2735: 2721: 2718: 2665: 2662: 2661: 2660: 2659: 2658: 2585:for discussion 2571: 2565: 2564: 2563: 2562: 2561: 2560: 2559: 2558: 2557: 2538: 2537: 2536: 2535: 2534: 2502:Stanley Skewes 2483: 2479: 2474: 2469: 2447:David Eppstein 2418:as it does in 2390: 2354: 2353: 2352: 2351: 2350: 2349: 2348: 2347: 2346: 2345: 2344: 2343: 2342: 2341: 2340: 2339: 2338: 2305:David Eppstein 2278: 2277: 2276: 2272: 2261: 2257: 2249: 2248: 2247: 2244:idoneal number 2225: 2221: 2217: 2212: 2208: 2204: 2201: 2190:Leyland number 2186: 2175:2-almost prime 2173:(synonymously 2158: 2155: 2152: 2149: 2138: 2131: 2120:Hilbert number 2108:sorting number 2083:David Eppstein 2058: 2021: 1966:Leyland number 1961:indiscriminate 1957: 1956: 1955: 1914: 1900:David Eppstein 1863: 1859: 1858: 1857: 1856: 1855: 1835:, or even the 1816: 1808: 1799: 1747:David Eppstein 1699: 1698: 1697: 1696: 1682: 1665: 1664: 1647:Infobox number 1610: 1609: 1608: 1607: 1606: 1605: 1604: 1603: 1593:David Eppstein 1573: 1551:Leyland number 1537: 1536: 1535: 1521: 1497:David Eppstein 1465: 1450: 1449: 1448: 1436:kissing number 1424: 1417: 1414:Leyland number 1410: 1400: 1382:David Eppstein 1355: 1349: 1348: 1347: 1346: 1345: 1344: 1343: 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: 4499: 4488: 4485: 4484: 4482: 4469: 4465: 4461: 4456: 4455: 4454: 4450: 4446: 4442: 4441: 4440: 4436: 4432: 4428: 4427: 4426: 4425: 4421: 4417: 4413: 4409: 4405: 4401: 4393: 4385: 4381: 4377: 4373: 4372: 4371: 4370: 4369: 4368: 4363: 4359: 4355: 4351: 4346: 4345: 4344: 4341: 4338: 4334: 4329: 4328: 4327: 4326: 4322: 4318: 4313: 4311: 4304: 4300: 4297: 4296: 4295: 4292: 4290: 4286: 4280: 4275: 4272: 4270: 4267: 4266: 4265: 4260: 4256: 4253: 4251: 4247: 4244: 4243: 4242: 4236: 4224: 4220: 4216: 4211: 4210: 4209: 4205: 4201: 4197: 4193: 4189: 4185: 4181: 4180: 4179: 4175: 4171: 4167: 4164: 4163: 4162: 4158: 4154: 4149: 4148: 4147: 4144: 4141: 4137: 4136: 4135: 4134: 4130: 4126: 4122: 4118: 4114: 4107: 4103: 4099: 4095: 4090:<math: --> 4083: 4082: 4081: 4080: 4076: 4072: 4071:Michael Hardy 4068: 4060: 4056: 4052: 4048: 4044: 4041: 4037: 4033: 4032: 4031: 4030: 4027: 4024: 4020: 4016: 4012: 4008: 4004: 4000: 3996: 3992: 3988: 3984: 3976: 3970: 3966: 3962: 3958: 3954: 3953: 3952: 3948: 3944: 3940: 3936: 3935: 3934: 3933: 3929: 3925: 3921: 3918: 3911: 3904: 3900: 3895: 3892: 3888: 3884: 3880: 3877: 3874: 3870: 3864: 3860: 3856:, defined as 3855: 3849: 3841: 3835: 3831: 3827: 3826:Limit-theorem 3823: 3822: 3821: 3817: 3813: 3809: 3808: 3807: 3806: 3802: 3798: 3797:Michael Hardy 3791: 3788: 3785: 3780: 3774: 3770: 3766: 3762: 3758: 3754: 3750: 3746: 3742: 3738: 3735: 3733: 3732:sigma-compact 3729: 3726: 3724: 3723:sigma-algebra 3721: 3719: 3716: 3714: 3711: 3709: 3705: 3702: 3701: 3699: 3695: 3694: 3693: 3690: 3687: 3684: 3680: 3679: 3678: 3674: 3670: 3666: 3662: 3661: 3660: 3659: 3656: 3653: 3650: 3643: 3640: 3638: 3635: 3633: 3630: 3628: 3625: 3623: 3620: 3618: 3615: 3614: 3610: 3604: 3600: 3596: 3592: 3588: 3584: 3580: 3576: 3566: 3562: 3558: 3549: 3545: 3544: 3543: 3539: 3535: 3531: 3527: 3526:Stephen Smale 3523: 3519: 3515: 3511: 3507: 3506: 3505: 3502: 3501: 3497: 3496: 3491: 3487: 3483: 3480: 3477: 3473: 3469: 3465: 3460: 3459: 3458: 3454: 3450: 3444: 3438: 3437: 3436: 3433: 3430: 3426: 3422: 3421:Wiles theorem 3418: 3414: 3412: 3408: 3404: 3400: 3395: 3392: 3389: 3385: 3381: 3378: 3374: 3371: 3368: 3364: 3363: 3361: 3360: 3359: 3355: 3351: 3347: 3346: 3345: 3342: 3339: 3335: 3331: 3327: 3323: 3319: 3313: 3309: 3305: 3301: 3297: 3296: 3295: 3291: 3287: 3282: 3281: 3280: 3276: 3272: 3268: 3264: 3263: 3262: 3258: 3254: 3250: 3249: 3248: 3247: 3243: 3239: 3235: 3231: 3227: 3224: 3221: 3217: 3207: 3206: 3202: 3198: 3194: 3188: 3184: 3174: 3170: 3166: 3162: 3161: 3160: 3156: 3154: 3150: 3147: 3144: 3143: 3142: 3138: 3134: 3130: 3129: 3128: 3124: 3114: 3110: 3104: 3099: 3098: 3097: 3096: 3092: 3088: 3084: 3080: 3076: 3071: 3070: 3066: 3062: 3058: 3054: 3047: 3044: 3040: 3036: 3034: 3030: 3029: 3028: 3027: 3023: 3019: 3015: 3011: 3007: 3000: 2986: 2982: 2978: 2973: 2970: 2969: 2968: 2965: 2959: 2955: 2954: 2953: 2949: 2945: 2941: 2940: 2939: 2936: 2929: 2928: 2927: 2923: 2919: 2915: 2911: 2907: 2904: 2898: 2894: 2889: 2885: 2884:Weak topology 2881: 2877: 2873: 2869: 2868:Norm topology 2865: 2861: 2857: 2853: 2852: 2851: 2847: 2843: 2838: 2837: 2836: 2833: 2827: 2823: 2821: 2818: 2811: 2807: 2803: 2799: 2796: 2790: 2786: 2782: 2778: 2777: 2776: 2773: 2767: 2763: 2761: 2758: 2752: 2751: 2750: 2749: 2745: 2741: 2733: 2729: 2725: 2722: 2719: 2716: 2715: 2714: 2711: 2709: 2705: 2701: 2696: 2690: 2688: 2685:redirects to 2683: 2678: 2676: 2671: 2663: 2657: 2653: 2649: 2643: 2638: 2637: 2636: 2632: 2628: 2624: 2620: 2617: 2613: 2612: 2611: 2610: 2606: 2602: 2598: 2594: 2590: 2586: 2582: 2577: 2570: 2566: 2556: 2552: 2548: 2544: 2539: 2533: 2529: 2525: 2521: 2520: 2519: 2515: 2511: 2507: 2504:just because 2503: 2481: 2477: 2472: 2467: 2458: 2457: 2456: 2452: 2448: 2443: 2442: 2441: 2437: 2433: 2429: 2425: 2421: 2417: 2413: 2412: 2411: 2407: 2403: 2399: 2395: 2391: 2389: 2385: 2381: 2377: 2376: 2375: 2371: 2367: 2363: 2359: 2355: 2337: 2333: 2329: 2325: 2321: 2316: 2315: 2314: 2310: 2306: 2302: 2298: 2293: 2292: 2291: 2287: 2283: 2279: 2273: 2270: 2265: 2264: 2262: 2258: 2254: 2250: 2245: 2241: 2223: 2219: 2215: 2210: 2206: 2202: 2199: 2191: 2187: 2184: 2180: 2176: 2172: 2156: 2153: 2150: 2147: 2139: 2136: 2132: 2129: 2125: 2124:polite number 2121: 2117: 2113: 2109: 2105: 2101: 2100: 2098: 2094: 2093: 2092: 2088: 2084: 2079: 2074: 2073: 2072: 2068: 2064: 2059: 2056: 2051: 2050: 2049: 2045: 2041: 2037: 2019: 2009: 2004: 2003: 2002: 1998: 1994: 1989: 1988: 1987: 1983: 1979: 1975: 1971: 1967: 1962: 1958: 1954: 1950: 1946: 1941: 1939: 1938:prime factors 1935: 1931: 1927: 1924: 1921: 1915: 1911: 1910: 1909: 1905: 1901: 1897: 1893: 1889: 1888: 1887: 1883: 1879: 1874: 1871: 1867: 1864: 1860: 1854: 1850: 1846: 1842: 1838: 1834: 1830: 1826: 1822: 1814: 1809: 1805: 1800: 1798: 1794: 1790: 1786: 1782: 1778: 1774: 1770: 1766: 1762: 1758: 1757: 1756: 1752: 1748: 1744: 1740: 1737: 1733: 1732: 1731: 1727: 1723: 1719: 1718: 1717: 1716: 1712: 1708: 1704: 1695: 1691: 1687: 1683: 1681: 1677: 1673: 1669: 1668: 1667: 1666: 1663: 1659: 1655: 1648: 1641: 1640: 1639: 1638: 1634: 1630: 1624: 1623: 1619: 1615: 1602: 1598: 1594: 1589: 1588: 1587: 1583: 1579: 1574: 1570: 1569: 1568: 1564: 1560: 1556: 1552: 1547: 1546:Blum integers 1542: 1538: 1534: 1530: 1526: 1522: 1520: 1516: 1512: 1508: 1507: 1506: 1502: 1498: 1493: 1488: 1484: 1483: 1482: 1478: 1474: 1470: 1466: 1464: 1460: 1456: 1451: 1445: 1441: 1437: 1433: 1429: 1428:Monster group 1425: 1422: 1418: 1415: 1411: 1408: 1404: 1403: 1401: 1398: 1394: 1393: 1392: 1391: 1387: 1383: 1379: 1376: 1373: 1369: 1365: 1361: 1354: 1350: 1342: 1338: 1334: 1330: 1328: 1324: 1320: 1314: 1310: 1309: 1308: 1304: 1300: 1296: 1295: 1294: 1290: 1286: 1282: 1276: 1271: 1270: 1269: 1268: 1264: 1260: 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: 4398:The article 4397: 4314: 4307: 4293: 4281: 4278: 4263: 4240: 4111: 4064: 3991:Vulgar Latin 3980: 3956: 3916: 3909: 3902: 3898: 3890: 3886: 3882: 3862: 3858: 3845: 3794: 3760: 3756: 3741:sigma-finite 3708:σ-additivity 3697: 3646: 3547: 3499: 3494: 3442: 3423:redirect to 3222: 3213: 3191: 3103:TakuyaMurata 3083:Leibniz rule 3072: 3056: 3050: 3004: 2806:WP:TECHNICAL 2737: 2732:WP:TECHNICAL 2712: 2691: 2679: 2667: 2615: 2573: 2543:178_(number) 2428:178 (number) 2416:178 (number) 2394:178_(number) 2362:178_(number) 2358:177_(number) 2323: 2319: 2268: 2252: 2179:Blum integer 2055:177 (number) 2035: 2007: 1917: 1870:177 (number) 1837:golden ratio 1702: 1700: 1625: 1611: 1540: 1491: 1407:Blum integer 1374: 1364:177 (number) 1360:example diff 1357: 1353:177 (number) 1313:Fields Medal 1281:Fields Medal 1255:Fields Medal 1252: 1233: 1156: 1101: 1072: 1042: 987: 932: 877: 822: 767: 712: 657: 602: 547: 492: 437: 382: 327: 272: 217: 162: 107: 103:Sep–Dec 2004 99:Jan–Aug 2004 44: 4376:Jason Quinn 4350:WP:DIFFCAPS 4317:Jason Quinn 3879:isomorphism 3759:is about). 3622:Sigma-ideal 3534:SilverMatsu 3304:SilverMatsu 3271:SilverMatsu 3214:A new user 2648:SilverMatsu 2601:SilverMatsu 2593:SilverMatsu 2422:, I think. 2112:Ulam number 2104:evil number 1974:Ulam number 1918:"177 is an 1773:what it has 1492:interesting 1444:j-invariant 1333:SilverMatsu 1285:SilverMatsu 3943:XOR'easter 3627:Sigma-ring 3197:XOR'easter 2804:"much too 2642:XOR'easter 2627:XOR'easter 2510:XOR'easter 2432:XOR'easter 2238:. It is a 2133:177 is an 2102:177 is an 2040:XOR'easter 1978:XOR'easter 1789:XOR'easter 1654:XOR'easter 1559:XOR'easter 91:Motivation 4445:PatrickR2 4416:PatrickR2 4406:. Should 4337:jacobolus 4140:jacobolus 4094:PatrickR2 4067:this edit 4023:jacobolus 3812:JRSpriggs 3784:jacobolus 3669:PatrickR2 3632:σ-algebra 3557:Trovatore 3510:Trovatore 3476:jacobolus 3449:Trovatore 3429:jacobolus 3370:304537849 3350:Trovatore 3338:jacobolus 3320:I’d make 3253:Trovatore 2977:PatrickR2 2944:PatrickR2 2918:PatrickR2 2547:PatrickR2 2524:PatrickR2 2402:PatrickR2 2380:PatrickR2 2366:PatrickR2 2171:semiprime 2061:forward? 1926:semiprime 1923:composite 1672:JRSpriggs 1629:JRSpriggs 1525:PatrickR2 4481:Category 4460:Felix QW 3881:, it is 3686:1234qwer 3683:1234qwer 3652:1234qwer 3649:1234qwer 3495:Spinning 3367:ProQuest 3286:Gumshoe2 3238:Gumshoe2 3226:contribs 3018:D.Lazard 2842:Gumshoe2 2740:D.Lazard 2328:Gumshoe2 2282:Gumshoe2 2188:It is a 2063:Gumshoe2 1993:Gumshoe2 1945:Gumshoe2 1913:website. 1878:Gumshoe2 1804:Gumshoe2 1769:how much 1378:contribs 1299:Gumshoe2 1275:Gumshoe2 1259:Gumshoe2 24:‎ | 20:‎ | 4086:''n+2'' 4043:2214259 3713:σ-ideal 2972:Mgkrupa 2963:Mgkrupa 2934:Mgkrupa 2902:Mgkrupa 2831:Mgkrupa 2826:Mgkrupa 2816:Mgkrupa 2794:Mgkrupa 2771:Mgkrupa 2756:Mgkrupa 2728:Mgkrupa 2008:example 1936:as its 1775:on the 1763:" and " 1736:uncivil 1234:15 days 22:Archive 4188:P/poly 3887:unique 3873:unique 3871:), is 3842:Colons 3718:σ-ring 3553:point. 3332:or to 3057:at all 3010:WP:RfC 2251:(I am 1892:WP:ANI 1862:admin. 1845:Radlrb 1722:Radlrb 1707:Radlrb 1686:Radlrb 1614:Radlrb 1578:Radlrb 1511:Radlrb 1473:Radlrb 1455:Radlrb 1368:Radlrb 1362:). On 4308:with 4215:Kusma 4170:Kusma 3997:, or 3876:up to 3867:(see 3854:field 3500:Spark 3118:MarkH 2322:than 2269:makes 2036:early 1972:, an 1928:with 1896:WP:EL 1841:David 16:< 4464:talk 4449:talk 4435:talk 4420:talk 4380:talk 4358:talk 4321:talk 4283:the 4219:talk 4204:talk 4174:talk 4157:talk 4129:talk 4119:and 4098:talk 4075:talk 4065:See 4051:talk 4045:). — 4034:See 3965:talk 3947:talk 3928:talk 3905:+ 1) 3865:+ 1) 3830:talk 3816:talk 3801:talk 3769:talk 3757:that 3673:talk 3599:talk 3561:talk 3548:good 3538:talk 3528:and 3514:talk 3453:talk 3443:know 3419:and 3407:talk 3354:talk 3324:and 3308:talk 3302:. -- 3290:talk 3275:talk 3257:talk 3242:talk 3220:talk 3201:talk 3169:talk 3165:Taku 3146:Taku 3137:talk 3133:Taku 3115:. — 3091:talk 3087:Taku 3065:talk 3061:Taku 3022:talk 2981:talk 2948:talk 2922:talk 2846:talk 2744:talk 2692:But 2652:talk 2631:talk 2605:talk 2597:talk 2551:talk 2528:talk 2514:talk 2451:talk 2436:talk 2406:talk 2384:talk 2370:talk 2332:talk 2309:talk 2286:talk 2114:and 2087:talk 2067:talk 2044:talk 1997:talk 1982:talk 1968:, a 1949:talk 1932:and 1904:talk 1882:talk 1849:talk 1819:and 1793:talk 1783:and 1751:talk 1726:talk 1711:talk 1690:talk 1676:talk 1658:talk 1633:talk 1618:talk 1597:talk 1582:talk 1563:talk 1541:this 1529:talk 1515:talk 1509:Ok. 1501:talk 1477:talk 1459:talk 1386:talk 1372:talk 1337:talk 1331:).-- 1303:talk 1289:talk 1263: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 26:2022 4431:JBL 4340:(t) 4143:(t) 4026:(t) 3961:JBL 3924:JBL 3913:to 3896:of 3891:two 3883:not 3787:(t) 3581:to 3532:.-- 3492:). 3479:(t) 3466:or 3432:(t) 3384:doi 3341:(t) 3336:. – 3300:RfD 3232:to 3111:or 2870:, 2324:iff 2253:not 2200:177 2192:as 1920:odd 1813:240 1432:2.B 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 4483:: 4466:) 4451:) 4437:) 4422:) 4382:) 4360:) 4323:) 4301:→ 4257:→ 4248:→ 4221:) 4206:) 4190:? 4176:) 4159:) 4131:) 4100:) 4077:) 4053:) 4040:MR 3993:, 3989:, 3985:, 3967:) 3949:) 3930:) 3901:/( 3861:/( 3832:) 3818:) 3803:) 3771:) 3739:, 3730:, 3706:, 3700:: 3675:) 3601:) 3589:, 3563:) 3555:-- 3540:) 3516:) 3455:) 3447:-- 3409:) 3372:, 3356:) 3310:) 3292:) 3277:) 3259:) 3244:) 3216:廖培 3203:) 3171:) 3157:: 3139:) 3121:21 3093:) 3067:) 3037:: 3024:) 2983:) 2950:) 2924:) 2895:, 2882:, 2878:, 2874:, 2862:, 2848:) 2791:. 2746:) 2710:. 2689:. 2677:. 2654:) 2633:) 2625:. 2616:to 2607:) 2599:) 2553:) 2530:) 2516:) 2508:. 2482:34 2478:10 2473:10 2468:10 2453:) 2438:) 2408:) 2400:. 2386:) 2372:) 2334:) 2320:if 2311:) 2288:) 2154:59 2151:× 2089:) 2069:) 2046:) 1999:) 1984:) 1951:) 1934:59 1906:) 1884:) 1851:) 1833:24 1831:, 1829:15 1795:) 1787:. 1753:) 1728:) 1713:) 1692:) 1678:) 1660:) 1650:}} 1644:{{ 1635:) 1620:) 1599:) 1584:) 1565:) 1531:) 1517:) 1503:) 1479:) 1461:) 1419:A 1412:A 1405:A 1388:) 1366:, 1339:) 1329:." 1305:) 1291:) 1265:) 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:· 4462:( 4447:( 4433:( 4418:( 4378:( 4356:( 4319:( 4217:( 4202:( 4172:( 4155:( 4151:— 4127:( 4096:( 4073:( 4049:( 3963:( 3957:C 3945:( 3926:( 3920:. 3917:x 3915:− 3910:x 3903:x 3899:R 3863:x 3859:R 3828:( 3814:( 3799:( 3782:– 3767:( 3689:4 3671:( 3655:4 3611:σ 3597:( 3559:( 3536:( 3512:( 3451:( 3405:( 3396:) 3390:) 3386:: 3379:. 3352:( 3306:( 3288:( 3273:( 3255:( 3240:( 3223:· 3218:( 3199:( 3167:( 3135:( 3105:: 3101:@ 3089:( 3063:( 3020:( 2979:( 2946:( 2920:( 2866:, 2844:( 2742:( 2650:( 2644:: 2640:@ 2629:( 2603:( 2595:( 2549:( 2526:( 2512:( 2449:( 2434:( 2404:( 2382:( 2368:( 2330:( 2307:( 2284:( 2224:2 2220:7 2216:+ 2211:7 2207:2 2203:= 2157:, 2148:3 2085:( 2065:( 2042:( 2020:2 1995:( 1980:( 1947:( 1940:" 1930:3 1902:( 1880:( 1847:( 1817:8 1791:( 1749:( 1724:( 1709:( 1688:( 1674:( 1656:( 1631:( 1616:( 1595:( 1580:( 1561:( 1527:( 1513:( 1499:( 1475:( 1457:( 1384:( 1375:· 1370:( 1335:( 1301:( 1287:( 1277:: 1273:@ 1261:( 1242:. 71:) 65:e 58:t 51:v

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