Soupspoon wrote:Have you tried logarithms?

To be fair, taking the log of one of the variables would indeed map a square onto a rectangle.

- Sat Oct 27, 2018 7:24 pm UTC
- Forum: Mathematics
- Topic: Curve Filling a Rectangle
- Replies:
**21** - Views:
**6642**

Soupspoon wrote:Have you tried logarithms?

To be fair, taking the log of one of the variables would indeed map a square onto a rectangle.

- Sat Oct 27, 2018 7:20 pm UTC
- Forum: Mathematics
- Topic: Equivalency on Mutliple Intervals
- Replies:
**10** - Views:
**9075**

The best way to do this is that if f and g are functions with a particular property, hope that f-g also has that property. If that's the case, then your question becomes: If f is a function with property P, and f=0 on an interval, is f=0? I think analytic is the only class of functions for which thi...

- Sat Sep 08, 2018 7:15 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2042: "Rolle's Theorem"
- Replies:
**86** - Views:
**10478**

In Whitehead and Russel's Principia Mathematica, it takes at least 360* pages of dense mathematical foundation before addition is defined. I wouldn't be at all surprised if an even more modern attempt to build up an axiomatic mathematics takes even longer. Modern attempts to build up mathematics (s...

- Sun Aug 05, 2018 10:09 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2028: "Complex Numbers"
- Replies:
**48** - Views:
**6449**

Still I have seen them used in cases where you basically only do care about R 2 , like for 2-D graphics, which is kind of annoying because they have no 3-D equivalent so they're obviously not what you mean. Well, if you need to rotate an object in 2D then it's a bit of a pain, unless you write R 2 ...

- Sat Aug 04, 2018 5:09 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2028: "Complex Numbers"
- Replies:
**48** - Views:
**6449**

I just came here to point out that meta-abelian groups are already a thing, and it's not an abelian group that's so, like, meta. Also: First the complex plane is a connected set whereas two dimensional real numbers are not. Which topology are you placing on R^2? The product topology? The standard to...

- Fri May 18, 2018 8:04 pm UTC
- Forum: Mathematics
- Topic: A fourth type of average?
- Replies:
**9** - Views:
**4498**

The fourth type of average would I guess be the geometric mean, assuming that the arithmetic mean was your other one. If not, then you should read them the other way round.

- Sun May 06, 2018 9:13 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1989: "IMHO"
- Replies:
**111** - Views:
**16112**

I'm also confused (as someone who always pronounced 'gif' with a hard 'g') because most words starting with 'gi' use a hard 'g', don't they?

Off the top of my head:

Soft 'g': gin, giraffe, giblet, gist,

Hard 'g': gift, gill, girl, gib, gimp, gird, git.

Off the top of my head:

Soft 'g': gin, giraffe, giblet, gist,

Hard 'g': gift, gill, girl, gib, gimp, gird, git.

- Tue Oct 31, 2017 7:41 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1909:"Digital Resource Lifespan"
- Replies:
**61** - Views:
**8565**

This is why we need more monks majoring in computer science. Not the monks! They destroyed more classical works of science for their stupid fairy stories than fire and flood. OK, probably not that many, but many. Some Greek works only survive because the monk involved wasn't very good at washing th...

- Sat Aug 12, 2017 6:49 am UTC
- Forum: Mathematics
- Topic: Foolish question debunked. Move on, nothing to see.
- Replies:
**80** - Views:
**12038**

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. ...

- Fri Jul 07, 2017 8:55 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1859: "Sports Knowledge"
- Replies:
**44** - Views:
**7495**

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?

- Fri Jul 07, 2017 8:40 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1859: "Sports Knowledge"
- Replies:
**44** - Views:
**7495**

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...

- Wed Feb 08, 2017 9:14 am UTC
- Forum: Mathematics
- Topic: "There is an Exception to every rule"
- Replies:
**32** - Views:
**8127**

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?

- Mon Dec 26, 2016 12:29 pm UTC
- Forum: Mathematics
- Topic: Probability distribution on the power set of natural numbers?
- Replies:
**12** - Views:
**2756**

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

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

- 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:
**1952**

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...

- Sat Feb 07, 2015 2:33 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1483: "Quotative Like"
- Replies:
**83** - Views:
**13926**

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 &...

- Tue Nov 11, 2014 10:44 pm UTC
- Forum: Mathematics
- Topic: Congressional apportionment
- Replies:
**14** - Views:
**4256**

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...

- Thu Nov 06, 2014 11:36 pm UTC
- Forum: Mathematics
- Topic: how to calculate these intersections without having to write
- Replies:
**3** - Views:
**1980**

The first and third of these sets have equal size, and there's a nice bijection between them, if you can spot it.

- Thu Nov 06, 2014 11:05 pm UTC
- Forum: Mathematics
- Topic: Multiply 2 terminating numbers and get a repeating decimal?
- Replies:
**6** - Views:
**2810**

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...

- Wed Oct 01, 2014 8:40 pm UTC
- Forum: Mathematics
- Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
- Replies:
**42** - Views:
**10498**

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...

- Fri Aug 08, 2014 11:40 am UTC
- Forum: Mathematics
- Topic: is mathematics a religion?
- Replies:
**82** - Views:
**15379**

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...

- Sat May 31, 2014 12:46 pm UTC
- Forum: Mathematics
- Topic: hypothesis on primes
- Replies:
**9** - Views:
**4359**

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...

- Thu Apr 24, 2014 11:02 pm UTC
- Forum: Mathematics
- Topic: how many ways-married couples
- Replies:
**7** - Views:
**2812**

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...

- Fri Mar 14, 2014 5:05 am UTC
- Forum: Mathematics
- Topic: algebraic degree of sin(1 degree)
- Replies:
**4** - Views:
**2573**

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 ...

- Thu Feb 27, 2014 11:03 am UTC
- Forum: Mathematics
- Topic: Axiomatic mathematics has no foundation
- Replies:
**158** - Views:
**33429**

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.

- Thu Feb 27, 2014 10:58 am UTC
- Forum: Mathematics
- Topic: A probability(?) problem
- Replies:
**13** - Views:
**3805**

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 ...

- Sun Feb 23, 2014 3:03 pm UTC
- Forum: Mathematics
- Topic: A probability(?) problem
- Replies:
**13** - Views:
**3805**

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 ...

- Fri Feb 14, 2014 9:50 pm UTC
- Forum: Mathematics
- Topic: quarkcosh1's math coincidences thread
- Replies:
**32** - Views:
**8385**

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...

- Fri Feb 14, 2014 10:29 am UTC
- Forum: Mathematics
- Topic: quarkcosh1's math coincidences thread
- Replies:
**32** - Views:
**8385**

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 ...

- Fri Jan 24, 2014 9:40 am UTC
- Forum: Mathematics
- Topic: y = sum of subset of divisors of x
- Replies:
**2** - Views:
**1992**

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...

- Mon Nov 04, 2013 10:53 pm UTC
- Forum: Mathematics
- Topic: Permutations and Combinations
- Replies:
**7** - Views:
**2099**

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?

- Mon Nov 04, 2013 10:42 am UTC
- Forum: Mathematics
- Topic: Permutations and Combinations
- Replies:
**7** - Views:
**2099**

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...

- Sun Sep 08, 2013 9:59 am UTC
- Forum: Mathematics
- Topic: Group theory II
- Replies:
**46** - Views:
**13372**

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...

- Fri Sep 06, 2013 9:57 pm UTC
- Forum: Mathematics
- Topic: Group theory II
- Replies:
**46** - Views:
**13372**

I ran the code, and R fails to be confluent.

- Fri Sep 06, 2013 9:25 pm UTC
- Forum: Mathematics
- Topic: basic doubt about groups
- Replies:
**19** - Views:
**4801**

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 ...

- Sun Aug 25, 2013 12:36 pm UTC
- Forum: Mathematics
- Topic: When will $1 be the smallest denomination?
- Replies:
**51** - Views:
**9897**

gmalivuk wrote:It is a fake boxing stance.

Aha. I still prefer the mid fist pump explanation...

- Sun Aug 25, 2013 12:45 am UTC
- Forum: Mathematics
- Topic: When will $1 be the smallest denomination?
- Replies:
**51** - Views:
**9897**

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...

- 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:
**3779**

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...

- 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:
**3779**

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...

- 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:
**3779**

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....

- 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:
**3779**

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...