Search found 233 matches

by DavCrav
Sat Aug 12, 2017 6:49 am UTC
Forum: Mathematics
Topic: Foolish question debunked. Move on, nothing to see.
Replies: 80
Views: 4579

Re: Foolish question debunked. Move on, nothing to see.

Can I just intercede here? I think BT is being misunderstood a bit somewhere on here. Here's a real-world analogy for BT. You buy some electrical appliance, unbox it, untie the cable, and then you cannot seem to get the whole lot inside the box again no matter what you try. Obviously this isn't BT. ...
by DavCrav
Fri Jul 07, 2017 8:55 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1859: "Sports Knowledge"
Replies: 44
Views: 3592

Re: 1859: "Sports Knowledge"

Because the city name is the brand, that's worth money. And if they moved for money, why would they throw money away by de-branding themselves?
by DavCrav
Fri Jul 07, 2017 8:40 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1859: "Sports Knowledge"
Replies: 44
Views: 3592

Re: 1859: "Sports Knowledge"

I might well be wrong about this, not being from the US, but I thought all these teams played in different areas because they keep threatening to leave $CITY unless it throws tax breaks and new stadia at them, and every so often a city calls their bluff, so they head off to wherever the sun is shini...
by DavCrav
Wed Feb 08, 2017 9:14 am UTC
Forum: Mathematics
Topic: "There is an Exception to every rule"
Replies: 32
Views: 5655

Re: "There is an Exception to every rule"

That's not a rule, that's a tautology.


Fine, for every prime p, and every integer a prime to p, a raised to power p minus a is divisible by p. Not a tautology, definitely no exceptions. Happy now?
by DavCrav
Mon Dec 26, 2016 12:29 pm UTC
Forum: Mathematics
Topic: Probability distribution on the power set of natural numbers?
Replies: 12
Views: 1882

Re: Probability distribution on the power set of natural numbers?

You should be able to apply Kolmogorov's zero-one law:

https://en.wikipedia.org/wiki/Kolmogorov's_zero%E2%80%93one_law

The Hewitt--Savage zero-one law is even better for this problem I would think.

https://en.wikipedia.org/wiki/Hewitt%E2%80%93Savage_zero%E2%80%93one_law
by DavCrav
Mon Dec 26, 2016 12:21 pm UTC
Forum: Mathematics
Topic: Can't keep up with all the math behind machine learning
Replies: 3
Views: 1378

Re: Can't keep up with all the math behind machine learning

I want to know how something works on a deeper level when I use it, otherwise I feel dissatisifed and "stupid". This page on Sparse Coding makes absolutely no sense to me in terms of the math: http://ufldl.stanford.edu/wiki/index.php/Sparse_Coding . It's not that it doesn't make sense, it...
by DavCrav
Sat Feb 07, 2015 2:33 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1483: "Quotative Like"
Replies: 83
Views: 11314

Re: 1483: "Quotative Like"

Most people are, frankly, quite abysmal at quoting accurately from memory. Hence it is usually more correct to say “She was like” than “She said”, because most of the time she didn’t actually say precisely what is claimed, but only something broadly similar. So it's basically a shorter version of &...
by DavCrav
Tue Nov 11, 2014 10:44 pm UTC
Forum: Mathematics
Topic: Congressional apportionment
Replies: 14
Views: 3822

Re: Congressional apportionment

That's interesting (though having spent quite a bit of time thinking on election methods, not overly surprising. Impossibility theorems seem to be the name of the game). I'd definitely like to look closer at the claim that every divisor method violates quota, and I don't particularly trust rangevot...
by DavCrav
Thu Nov 06, 2014 11:36 pm UTC
Forum: Mathematics
Topic: how to calculate these intersections without having to write
Replies: 3
Views: 1818

Re: how to calculate these intersections without having to w

The first and third of these sets have equal size, and there's a nice bijection between them, if you can spot it.
by DavCrav
Thu Nov 06, 2014 11:05 pm UTC
Forum: Mathematics
Topic: Multiply 2 terminating numbers and get a repeating decimal?
Replies: 6
Views: 2416

Re: Multiply 2 terminating numbers and get a repeating decim

If you have two numbers a and b that have a terminating n-ary expansion, then so does their product. The quick way to see this is to multiply a and b by a suitably large power of the base so that they become integers, then product them to get an integer, obviously. Dividing by the (square of the) su...
by DavCrav
Wed Oct 01, 2014 8:40 pm UTC
Forum: Mathematics
Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
Replies: 42
Views: 8908

Re: The Ironic Paradox of Normalcy [Is my argument sound?]

OK, speaking as a professional mathematician, if a potential student put that under my nose I'd yell "CRANK!" and run. The reason? A wall of text posing as something mathematical and talking about non-mathematical concepts, naming Cantor, this definitely spikes my crank-ometer. Don't do it...
by DavCrav
Fri Aug 08, 2014 11:40 am UTC
Forum: Mathematics
Topic: is mathematics a religion?
Replies: 82
Views: 13415

Re: is mathematics a religion?

And actually, for a person with zero formal training, that's pretty good. I think we could all profit from a mutual open exchange of ideas here. I think he could profit from learning a bit about the marvels that the pros have discovered in the past 2500 years. And I thing we can profit from a fresh...
by DavCrav
Sat May 31, 2014 12:46 pm UTC
Forum: Mathematics
Topic: hypothesis on primes
Replies: 9
Views: 4053

Re: hypothesis on primes

First,a (late) thank to >-) for his answer Then,I 'd like to put the following thoughts under discussion by anyone who might care (all numbers are natural): 1.Let p b a prime. Between two succesive multiples of p 2 (that is between kp 2 and (k+1)p 2 ), you can always find exactly p-1 numbers d such...
by DavCrav
Thu Apr 24, 2014 11:02 pm UTC
Forum: Mathematics
Topic: how many ways-married couples
Replies: 7
Views: 2528

Re: how many ways-married couples

Hello!!! Could you help me at the following exercise? With how many ways can we choose a man and a woman that are not married to each other from n married couples? I thought that it is (n-1) n ,but I am not sure.Can you tell me if it is right? So firstly, how many ways are there of choosing a man a...
by DavCrav
Fri Mar 14, 2014 5:05 am UTC
Forum: Mathematics
Topic: algebraic degree of sin(1 degree)
Replies: 4
Views: 2311

Re: algebraic degree of sin(1 degree)

Since totient(180) = 48 (totient being the number of numbers coprime to 180 less than one 180 - or the order of the multiplicative group mod 180), this makes sense; the minimum polynomial is presumably the 180th cyclotomic polynomial (though I don't know how one would prove that) If it's true that ...
by DavCrav
Thu Feb 27, 2014 11:03 am UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 30063

Re: Axiomatic mathematics has no foundation

Forest Goose wrote:Presburger Arithmetic is consistent and complete.


So is the theory of algebraically closed fields. Just thought I'd throw in some actual mathematics to try to stem the tide of pseudo-philosophical manure in this thread.
by DavCrav
Thu Feb 27, 2014 10:58 am UTC
Forum: Mathematics
Topic: A probability(?) problem
Replies: 13
Views: 3365

Re: A probability(?) problem

I don't see how that follows at all. It seems like you're implicitly relying on some other distribution information to make that statement about the size of X? That was pretty much my thought too. Unless you are implicitly assuming that X takes a form similar to {1, 2, ..., n} then I don't see how ...
by DavCrav
Sun Feb 23, 2014 3:03 pm UTC
Forum: Mathematics
Topic: A probability(?) problem
Replies: 13
Views: 3365

Re: A probability(?) problem

Here's another reason why you might say 2: Change the question slightly to: let X be a finite set of natural numbers. Choose an element randomly from X with uniform probability (can be done since X is finite). This element is 2. What does this tell you about X? Well, one obvious thing that it tells ...
by DavCrav
Fri Feb 14, 2014 9:50 pm UTC
Forum: Mathematics
Topic: quarkcosh1's math coincidences thread
Replies: 32
Views: 7311

Re: quarkcosh1's math coincidences thread

I'd suggest that before delving into details like this, try to determine whether quarkcosh knows anything whatsoever about the Monster group apart from the frequency with which certain numbers show up in that Wikipedia list. Just because someone is stringing together meaningless concepts without an...
by DavCrav
Fri Feb 14, 2014 10:29 am UTC
Forum: Mathematics
Topic: quarkcosh1's math coincidences thread
Replies: 32
Views: 7311

Re: quarkcosh1's math coincidences thread

The = means approximately equal. I was looking at the subgroups of the monster group and 11 appears 6 times which seems kind of high since numbers slightly lower than it don't appear as many times. The best explanation I can think of as to why that is is because pi^3 - e^3 = 11 but I can't explain ...
by DavCrav
Fri Jan 24, 2014 9:40 am UTC
Forum: Mathematics
Topic: y = sum of subset of divisors of x
Replies: 2
Views: 1853

Re: y = sum of subset of divisors of x

In essence, you just want to know which subsets of X can add together to make a number n. I don't know the most efficient algorithm to do this, but I needed this to solve a problem about possible decompositions of modules for algebraic groups, and thought up the following easy recursive algorithm. f...
by DavCrav
Mon Nov 04, 2013 10:53 pm UTC
Forum: Mathematics
Topic: Permutations and Combinations
Replies: 7
Views: 1898

Re: Permutations and Combinations

Hmm. So independent and mutually exclusive look like the same thing in this case. In which case, it isn't robustened, or whatever somebody earlier said. If they are different things, what is the difference in the context of combinations?
by DavCrav
Mon Nov 04, 2013 10:42 am UTC
Forum: Mathematics
Topic: Permutations and Combinations
Replies: 7
Views: 1898

Re: Permutations and Combinations

I don't think that's clear. You do need independence of some sort, not just not mutually exclusive. Here is an example, in the spirit of the OP: we'll take clothing and sex. There are (generically) two options for sex, but depending on the choice of sex, only certain clothing options might be availa...
by DavCrav
Sun Sep 08, 2013 9:59 am UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 12678

Re: Group theory II

I put an extra zero on the end of MaxRelations but it seemed to take a long time and then my connection died and my SSH session closed. The trouble with things like this is, there's no reason to think that it will take less storage than there are atoms in the Universe...
by DavCrav
Fri Sep 06, 2013 9:57 pm UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 12678

Re: Group theory II

I ran the code, and R fails to be confluent.
by DavCrav
Fri Sep 06, 2013 9:25 pm UTC
Forum: Mathematics
Topic: basic doubt about groups
Replies: 19
Views: 4540

Re: basic doubt about groups

The integers under addition are finitely generated and are not a product of cyclic groups. I'm genuinely curious what definition of cyclic you use that excludes Z, because it can't be "a group other than Z which is generated by one element". E.g., a group G is cyclic if there exists x in ...
by DavCrav
Sun Aug 25, 2013 12:36 pm UTC
Forum: Mathematics
Topic: When will $1 be the smallest denomination?
Replies: 51
Views: 8499

Re: When will $1 be the smallest denomination?

gmalivuk wrote:It is a fake boxing stance.


Aha. I still prefer the mid fist pump explanation...
by DavCrav
Sun Aug 25, 2013 12:45 am UTC
Forum: Mathematics
Topic: When will $1 be the smallest denomination?
Replies: 51
Views: 8499

Re: When will $1 be the smallest denomination?

This is just a general question gmalivuk, but your photo looks like one of the following three things are happening: 1) You are dancing. 2) You are mid fist pump. 3) You are attempting (badly) a boxing stance. I was just interested as to which. I have nothing of value (ha!) to add to this thread, by...
by DavCrav
Sun Aug 25, 2013 12:42 am UTC
Forum: Mathematics
Topic: S subset N, exists an r in N such that if r in S then S=N
Replies: 14
Views: 3376

Re: S subset N, exists an r in N such that if r in S then S=

Anyway I do think that we often fail to give due respect to the awesome power of the universal quantifier. It lets us quantify over uncountable sets, most of whose members we could never name. That's a lot of power ... use it wisely! :-) Luckily I rarely have to invoke uncountable anything in my re...
by DavCrav
Sat Aug 24, 2013 4:24 pm UTC
Forum: Mathematics
Topic: S subset N, exists an r in N such that if r in S then S=N
Replies: 14
Views: 3376

Re: S subset N, exists an r in N such that if r in S then S=

This sort of thing is OK in a nice set like the natural numbers, but suppose we replace N by R. Now this sentence becomes a bit more interesting. Let S be the subset of all definable numbers. This can mean definable in *any way*: by computer programs, by algorithms, using words, anything reasonable...
by DavCrav
Fri Aug 23, 2013 10:09 pm UTC
Forum: Mathematics
Topic: S subset N, exists an r in N such that if r in S then S=N
Replies: 14
Views: 3376

Re: S subset N, exists an r in N such that if r in S then S=

This sort of thing is OK in a nice set like the natural numbers, but suppose we replace N by R. Now this sentence becomes a bit more interesting. Let S be the subset of all definable numbers. This can mean definable in *any way*: by computer programs, by algorithms, using words, anything reasonable....
by DavCrav
Fri Aug 23, 2013 8:49 pm UTC
Forum: Mathematics
Topic: S subset N, exists an r in N such that if r in S then S=N
Replies: 14
Views: 3376

Re: S subset N, exists an r in N such that if r in S then S=

The first line says: let S be a subset of N, so you have a fixed subset before you start. It's the difference between the two sentences: 1) For any number x, there is a number y such that y is larger than x. 2) There is a number y such that, for any number x, y is larger than x. Since S is chosen to...
by DavCrav
Thu Aug 22, 2013 6:41 pm UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 12678

Re: Group theory II

Cool. Can you check whether the group <a,b|a 2 , b 3 , (ab) 7 , [a,b] 10 , ([a,b] 4 b) 7 > is infinite? I just found out that when I ask for the order, and magma says 0, it does not mean infinite, it means it does not know. Therefore the online magma calculator is of no use to this problem. Also, i...
by DavCrav
Thu Aug 22, 2013 3:58 pm UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 12678

Re: Group theory II

Wait, so do you have magma (the real version not the online calculator)? Yes. I am a professional mathematician, so I have this sort of access, along with my own server to run this stuff on. Also, for 1) Thanks for proving that the Janko group J 1 is in fact a quotient of the group <a,b|a 2 , b 3 ,...
by DavCrav
Wed Aug 21, 2013 11:43 am UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 12678

Re: Group theory II

In an infinite group? Not that I know of. It seems to me that even in a finitely presented group, there could be infinitely many normal subgroups of bounded order... (Don't quote me on this.) This is false. In any finitely generated group, there are only finitely many subgroups of a given index. Ed...
by DavCrav
Thu Mar 14, 2013 9:25 am UTC
Forum: Mathematics
Topic: Groups & Their Presentations
Replies: 10
Views: 1994

Re: Groups & Their Presentations

While what letterX and stewbasic are saying is technically true, in reality your problem is much more tractable, since you don't want to change the generators. In this case it is a case of applying Tietze transformations to see whether one may reduce the word, and Magma has done that for you in the ...
by DavCrav
Wed Mar 13, 2013 6:46 pm UTC
Forum: Mathematics
Topic: Groups & Their Presentations
Replies: 10
Views: 1994

Re: Groups & Their Presentations

I typed the group into Magma and applied ReduceGenerators to it, and it came up with two relations for your group, namely b^-2aba^-1b^-1a^-1b^2a and b^-1ab^-1a^-1baba^-1b^-1aba^-1, so that G=<a,b|b^-2aba^-1b^-1a^-1b^2a,b^-1ab^-1a^-1baba^-1b^-1aba^-1>, with the same generators as before. Magma refuse...
by DavCrav
Sat Feb 02, 2013 2:58 pm UTC
Forum: Mathematics
Topic: Next great mathematical invention
Replies: 17
Views: 3625

Re: Next great mathematical invention

Yeah, the Laplace example is great. Nothing that was discovered in relativity and quantum theory could be said to have been "hiding in" the work he was familiar with. It was all quite novel. I cannot find such a quote by Laplace. On the contrary: What we know is not much. What we do not k...
by DavCrav
Sat Feb 02, 2013 2:31 pm UTC
Forum: Mathematics
Topic: Next great mathematical invention
Replies: 17
Views: 3625

Re: Next great mathematical invention

Carrying on the thought of fishfry, since calculus we had analysis, set theory (ZFC, GB, etc.), then category theory, and from what I can gather, although I'm not an expert on this, intensional dependent type theory. And that's just in foundations of mathematics.Entirely new fields of mathematics ha...
by DavCrav
Mon Oct 29, 2012 10:31 am UTC
Forum: Mathematics
Topic: group theory
Replies: 64
Views: 23178

Re: group theory

There's an online Magma calculator here: http://magma.maths.usyd.edu.au/calc/ I doubt if the SmallGroup database goes that far though. The paper that constructs all such groups is by A.E. Western, called Groups of Order p3q, which appeared in Proc. LMS back in 1898. The description is pretty complic...

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