805:
American-English are either the same or very similar. If I had known that at the time I believe I would have got a higher score. So my second question is, how much difference would getting one (or two, or three) questions right or wrong make to the percentile score? I imagine that towards the tails of ability, the wrong answer to one question makes much more difference to the percentile score than it does nearer the average. Thanks.
1772:
That's false history that a lot of people have unfortunately heard. No, set theory was started by Cantor, before the paradoxes were discovered, and the initial motivations came from real analysis. The paradoxes don't really have anything to do with formalization versus not-formalization; they have to
1725:
to be. What set theory provides is a common framework, making it easier to apply techniques from one branch of mathematics to problems from a different branch. I think of it as sort of "the operating system of mathematics". Different operating systems are certainly possible, but this one works pretty
796:
Many years ago I did a GMAT test, and I do remember my score was at the 86th. percentile. What would my actual score have been please? Although I did go to business school in the UK and got a MBA, I'm just curious if I had a good enough score to have gone to the best known business schools mentioned
1793:
I view math as an upside down pyramid. At the very top there are all the applications – the math that is “practical”. However, that builds on the other math, such as set theory, which is much closer to the base than most things you’ll find “practical”. Without it, much of the “practical” math would
1702:
Most things in maths are defined in terms of sets. Whether you consider that "practical" or not is a matter of semantics, I guess. For example, a group is defined as a set with an operation satisfying certain axioms - you couldn't have group theory without set theory, and group theory certainly has
692:
Thank you both. The identity theorem artice told me (if I understood the article properly), says that if there are two analytic functions and the set where they agree possesses an accumulation point in the domain then they are identical. That's fine but the original question was does there exist an
1729:
Those who study set theory, of course, are rarely thinking about the fact (even though it's arguably true) that their work may give theoretical clarity to some aspect of some field of pure mathematics that may have applications in some other field of pure mathematics that may have applications in
911:
for the z-score which is associated with 100 minus the
Percentile (or above Z in the link provided), and this figure will be used to find the proportion in the tail (or above Z). So for this example, it is the 86th percentile so we need to look for 14% (or .14) in the tail (or above the z) which
804:
On a side note, I am
British and during the test I was rather startled by having to answer questions about the grammar of American-English. So I tried to guess what a typical (stereotypical movie) American would say. Subsequently, I have found out that the grammar of British-English and
1744:
Well, you don't have to explicitly mention sets, but if you have group theory and just strip out all the stuff about operations, you'll find you've suddenly invented set theory. You wouldn't necessarily end up ZF set theory, but you would have something basic theory about sets.
634:
The domain is the set of complex numbers. f has only been defined on a restricted set of 1/2n and 1/2n+1. The question is that can there be an analytic f defined on whole of C so that whatever its values on other complex numbers are, they are 1/2n on the given
1346:
1641:
1679:
I'm not "dissing" the theory here. I don't mind if the set theory is useful for purely theoretical purposes. From what I've seen, the set theory is used mainly for defining and proving various other math concepts down to the most basic elements.
1817:
uses set theory now and then, among various other mathematical formalisms. Although still a kind of theory, PLs theory does have a fairly close connection to at least some kinds of programming-language design, and therefore practical implications.
527:(this is essentially what the isolated zeros principle says). Thus f is determined by its values on the set {1/2n|n in N}. Have you been taught (a form of) the isolated zeros principle? If not, I would call this an unfair question.
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On another note, what is practical? I’d include being a research or teaching professor of set theory practical. Thus it is useful for making a living for the few people lucky enough to be a professor of set theory.
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may have a derivation starting on 16-20; still reading it to see if it skips any steps. One thing I've noticed is that all of these sites seem to put different limits on the integral in the equation for
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604:. In that case the domain we are talking about is then a set of isolated points, is it not? Wouldn't that mean there are no accumulation points and such a proof cannot hold? --
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602:
574:
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1456:
875:
Correction, you said 86th percentile and for some reason I looked up the 84th percentile. Your score in the 86th percentile (z-score ~1.08) is around 641. Sorry for the error.--
1541:
503:
771:
Thanks for the identity theorem link; I knew we had an article on the result I know as the isolated zeros principle, but I'd completely forgotten where it was hiding.
291:
405:
1763:
I don't think it's useful. It was really created to formalize mathematics after some paradoxes about sets were discovered and people wondered how to solve them. –
1526:
I think that lecture note has a derivation that's good enough for me. Also, in this formulation of the problem, I'm pretty sure the equation should actually be:
25:
85:
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
1039:
801:
article. When I did the test, years before the internet was invented, I had no idea of how good my score was compared with any entrance requirements.
1730:
very-slightly-applied mathematics that ... eventually makes a minuscule contribution to building some improved "smart flange" in the year 2721. --
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37:
907:
Since these sorts of tests are assumed to be normally distributed: you look at the percentile score (86th percentile), check your handy
1721:
have group theory without set theory -- the fact that groups are standardly defined as certain kinds of sets, today, doesn't mean they
187:
936:, but I think I didn't put the question in the right form to catch the interest of people who normally watch the math reference desk.
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841:
Also, answering one or two questions more might or might not affect your percentile score. It depends on the rest of the candidates.--
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article the mean for 2005/2006 is 533 with a standard deviation of around 100. So your score would be around 632.--
757:
That f is the identity which cannot be since f ( 1/(2n+1) ) = 1/2n. So there exists no such function. Thank you.--
609:
149:
146:
This is my attempt:Suppose an analytic function satisfying the above conditions exist. Then f is continuous. As
86:
17:
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1007:
1341:{\displaystyle \mathbf {W} _{c}=\int _{0}^{\infty }e^{\mathbf {A} t}\mathbf {BB} ^{T}e^{\mathbf {A^{T}} t}dt}
897:
816:
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1636:{\displaystyle \mathbf {W} _{c}=\int _{0}^{\tau }e^{\mathbf {A} t}\mathbf {BB} ^{T}e^{\mathbf {A^{T}} t}dt}
1372:
724:=1. The function g(z) = z has this property as well. What does the identity theorem tell you about this? –
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1841:, which may be useful in keeping your aeroplane from dropping out of the sky because of an overlooked
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and didn't get very far, because I couldn't figure out how to put in the constraints. I kept getting
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I'm not sure if I should just give the answer, but the fact that the zeros of an analytic function
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and that the improper integral is used to study the properties of the system more generally.
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The point is that an analytic function is determined by its values on any set with an
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1111:{\displaystyle \min _{\mathbf {u} }\int _{0}^{\tau }\|\mathbf {u} (t)\|_{2}^{2}dt}
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Whatever your score was, it was better then 86% of the rest of the candidates.--
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analytic function or not. It didn't ask whether the function is unique or not?--
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119:
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1505:
1405:, which is obviously wrong. I think the answer must have something to do with
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that did not come out in extensive testing. It is also used in the theory of
548:
I'm confused. I can see this is true if the definition of f holds for all
74:
1413:, and I would be very interested in a complete answer to this question. —
1232:{\displaystyle \mathbf {x} _{0}^{T}\mathbf {W} _{c}^{-1}\mathbf {x} _{0}}
892:
Thanks, how do you get from the percentile score to the z score please?
995:{\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {Ax} +\mathbf {Bu} }
576:, but you imply it is also true if the definition applies only for all
372:{\displaystyle f({\frac {1}{2n+1}})={\frac {1}{2n}}\rightarrow f(0)=0}
723:
Assume there is a function f such that f(1/2n) = 1/2n for all n : -->
1429:
doesn't answer my question but does at least show that you can use
251:{\displaystyle f({\frac {1}{2n}})={\frac {1}{2n}}\rightarrow f(0)}
463:{\displaystyle {\frac {1}{2n+1}}<\epsilon <{\frac {1}{2n}}}
1849:. Neither is "deep" use in any sense, it is mainly elementary, "
858:
798:
507:
If f was real valued it is obvious but as f is complex valued so
1470:
on this topic but it states the equations without derivation.
79:
Welcome to the
Knowledge Mathematics Reference Desk Archives
1813:
I guess it's arguable whether it's "practical" itself, but
111:
Does there exist an analytic function f on C such that:
108:
Can any one please help me with the following question:
857:
86th percentile is a z-score around 0.99 and from our
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1161:{\displaystyle \mathbf {x} (\tau )=\mathbf {x} _{0}}
1354:. but I don't know how to derive it. Any advice?
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939:Given a system of linear differential equations:
1675:Is the Set theory useful for anything practical?
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1777:intuitive notion rather than some wrong one. --
114:f(1/2n) = f ( 1/(2n+1) ) = 1/2n for all n: -->
8:
1726:well, and has intrinsic attractions as well.
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1070:
177:{\displaystyle {\frac {1}{2n}}\rightarrow 0}
1371:Okay, I tried to attack this with standard
912:corresponds roughly to a z-score of 1.08.--
1466:to meet the boundary conditions. There's
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1504:, so the ones I put may not be right.
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663:Perhaps we should mention that the
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597:{\displaystyle n\in \mathbb {N} }
569:{\displaystyle n\in \mathbb {R} }
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1411:Hamilton-Jacobi-Bellman equation
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667:is useful for such questions. –
509:I am not sure how to proceed.--
1407:Pontryagin's minimum principle
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1833:Set theory is also used in
1815:programming language theory
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1703:practical applications. --
1472:This Stanford lecture note
470:. I now want to show that
1462:there) to get a value of
792:GMAT score as percentile
18:Knowledge:Reference desk
1858:22:15, 3 May 2008 (UTC)
1828:13:42, 3 May 2008 (UTC)
1808:19:21, 2 May 2008 (UTC)
1787:18:24, 2 May 2008 (UTC)
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1755:19:32, 2 May 2008 (UTC)
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1004:with initial condition
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645:06:09, 3 May 2008 (UTC)
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128:09:21, 2 May 2008 (UTC)
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286:{\displaystyle f(0)=0}
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87:current reference desk
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118:Much appreciated--
1853:" set theory. --
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1686:comment added by
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909:unit normal table
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1415:Keenan Pepper
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1387:
1374:
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1056:
1035:
1016:
1002:
981:
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964:
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935:
929:Derivation of
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923:
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906:
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764:
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492:
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477:
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366:
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342:
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321:
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308:
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280:
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98:
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80:
77:
76:
68:
61:
57:
53:
47:
42:
39:
35:
27:
23:
19:
1839:verification
1812:
1774:
1722:
1718:
1678:
1463:
1459:
1356:
1349:
1243:
1240:
1173:
1170:
1122:
1119:
1036:
1003:
941:
938:
932:
894:80.2.197.130
891:
813:80.0.108.213
803:
795:
726:
725:
669:
668:
506:
135:are isolated
117:
113:
110:
107:
94:
78:
1682:—Preceding
807:—Preceding
258:. But then
26:Mathematics
1717:Well, you
1468:a wikibook
773:Algebraist
529:Algebraist
406:0}" /: -->
139:Algebraist
1800:GromXXVII
1779:Trovatore
1732:Trovatore
1427:This site
50:<<
1820:Delirium
1684:unsigned
1458:(called
914:droptone
877:droptone
863:droptone
809:unsigned
728:King Bee
671:King Bee
383:0}": -->
293:. Also,
24: |
22:Archives
20: |
1855:Lambiam
1765:b_jonas
1409:or the
797:in the
89:pages.
1241:where
843:Shahab
829:Shahab
759:Shahab
695:Shahab
637:Shahab
635:set.--
511:Shahab
120:Shahab
1851:naive
1775:right
1747:Tango
1719:could
1705:Tango
1657:moink
1506:moink
1358:moink
391:: -->
379:. If
99:May 2
69:: -->
67:May 3
63:: -->
62:: -->
46:May 1
44:<
16:<
1837:and
1824:talk
1804:talk
1783:talk
1751:talk
1736:talk
1723:have
1709:talk
1692:talk
1661:talk
1510:talk
1362:talk
918:talk
898:talk
881:talk
867:talk
859:GMAT
847:talk
833:talk
817:talk
799:GMAT
763:talk
699:talk
641:talk
610:talk
515:talk
443:<
437:<
124:talk
115:=1.
1045:min
184:so
60:Jun
56:May
52:Apr
1826:)
1818:--
1806:)
1785:)
1753:)
1745:--
1738:)
1711:)
1694:)
1663:)
1571:τ
1562:∫
1512:)
1364:)
1276:∞
1267:∫
1210:−
1168:.
1138:τ
1089:‖
1071:‖
1066:τ
1057:∫
924:--
920:)
900:)
883:)
869:)
849:)
835:)
819:)
765:)
701:)
643:)
612:)
587:∈
559:∈
517:)
505:.
484:ϵ
440:ϵ
400:0}
388:ϵ
349:→
234:→
169:→
126:)
58:|
54:|
1822:(
1802:(
1781:(
1749:(
1734:(
1707:(
1690:(
1659:(
1631:t
1628:d
1623:t
1617:T
1613:A
1607:e
1601:T
1596:B
1593:B
1586:t
1582:A
1577:e
1566:0
1558:=
1553:c
1548:W
1508:(
1490:c
1485:W
1464:u
1460:Q
1444:c
1439:W
1392:0
1388:=
1384:u
1360:(
1336:t
1333:d
1328:t
1322:T
1318:A
1312:e
1306:T
1301:B
1298:B
1291:t
1287:A
1282:e
1271:0
1263:=
1258:c
1253:W
1225:0
1220:x
1213:1
1205:c
1200:W
1193:T
1188:0
1183:x
1154:0
1149:x
1144:=
1141:)
1135:(
1131:x
1106:t
1103:d
1098:2
1093:2
1085:)
1082:t
1079:(
1075:u
1061:0
1050:u
1021:0
1017:=
1013:x
989:u
986:B
982:+
978:x
975:A
971:=
965:t
962:d
956:x
952:d
916:(
896:(
879:(
865:(
845:(
831:(
815:(
761:(
697:(
639:(
608:(
591:N
584:n
563:R
556:n
513:(
493:0
490:=
487:)
481:(
478:f
455:n
452:2
448:1
431:1
428:+
425:n
422:2
418:1
394:0
367:0
364:=
361:)
358:0
355:(
352:f
343:n
340:2
336:1
331:=
328:)
322:1
319:+
316:n
313:2
309:1
304:(
301:f
281:0
278:=
275:)
272:0
269:(
266:f
246:)
243:0
240:(
237:f
228:n
225:2
221:1
216:=
213:)
207:n
204:2
200:1
195:(
192:f
172:0
163:n
160:2
156:1
122:(
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