## Search found 251 matches

- Wed Jun 12, 2019 11:42 am UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**3319**

### Re: "tricky" factoring problem

I never met it at school in the UK, and I did a lot of maths, pretty much all the maths it was possible to take at school.

- Wed Jun 12, 2019 8:25 am UTC
- Forum: Mathematics
- Topic: "tricky" factoring problem
- Replies:
**20** - Views:
**3319**

### Re: "tricky" factoring problem

The rational roots test should be taught more often in, well, every place.

If a_n x^n+...+a_0 is a polynomial in Z[x], then any rational root of it is p/q, where p divides a_0 and q divides a_n.

Proof: Exercise.

If a_n x^n+...+a_0 is a polynomial in Z[x], then any rational root of it is p/q, where p divides a_0 and q divides a_n.

Proof: Exercise.

- Sat Jun 01, 2019 12:45 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2157: "Diploma Legal Notes"
- Replies:
**27** - Views:
**2868**

### Re: 2157: "Diploma Legal Notes"

TheEngineer wrote:J%r wrote:So can I erase the word 'the' from the dictionary?

Can I erase the word 'dictionary' from the dicsh ... diks ... oh that book with all the words ... ?

A lexicon?

- Sun May 19, 2019 1:33 pm UTC
- Forum: Mathematics
- Topic: Gaussian Primes etc
- Replies:
**1** - Views:
**1082**

### Re: Gaussian Primes etc

What you need is a Unique Factorization Domain, or UFD, then you define primes. In fact, primes and irreducibles can always be defined. An element x is prime if whenever x divides ab, x divides a or x divides b. An element x is irreducible if, whenever x=ab, then one of a and b is a unit. (A unit is...

- Thu May 16, 2019 10:05 am UTC
- Forum: Mathematics
- Topic: a recursive factoring algorithm?
- Replies:
**31** - Views:
**2262**

### Re: a recursive factoring algorithm?

Eebster the Great wrote:I thought the Fermat attack was another name for Wiener's attack since it used Fermat's Little Theorem.

A quick Google search suggests it's not just me. For example, this page also calls it Fermat's attack. I couldn't possibly comment on where I heard it called that.

- Wed May 15, 2019 9:08 am UTC
- Forum: Mathematics
- Topic: Most useful isomorphisms you know?
- Replies:
**6** - Views:
**2131**

### Re: Most useful isomorphisms you know?

The complex numbers and the algebraic closure of the p-adic rationals are isomorphic as fields. Very useful if you like l-adic cohomology.

- Wed May 15, 2019 9:06 am UTC
- Forum: Mathematics
- Topic: a recursive factoring algorithm?
- Replies:
**31** - Views:
**2262**

### Re: a recursive factoring algorithm?

FWIW, Fermat devised a factorization method that uses (a + b)(a - b) = a² - b². See https://en.wikipedia.org/wiki/Fermat%27s_factorization_method In its simplest form, Fermat's method might be even slower than trial division (worst case). Nonetheless, the combination of trial division and Fermat's ...

- Thu May 09, 2019 7:48 pm UTC
- Forum: Mathematics
- Topic: Why is the cosecant "co"?
- Replies:
**17** - Views:
**5965**

### Re: Why is the cosecant "co"?

the 'co' stands for complementary. It's the sine/secant/tangent of the complementary angle (i.e., pi/2-angle).

- Mon Jan 07, 2019 1:28 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2094: "Short Selling"
- Replies:
**44** - Views:
**10592**

### Re: 2094: "Short Selling"

The point is that Tesla should be going bankrupt. The short sellers are absolutely correct: fundamentally Tesla is completely screwed. Is it? It made $311m in profit last quarter and is sitting on $3b in cash reserves, up $731m. It reports a 20% profit margin on the Model 3's. Let's see it post a p...

- Sun Jan 06, 2019 1:40 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2094: "Short Selling"
- Replies:
**44** - Views:
**10592**

### Re: 2094: "Short Selling"

Hypothesis: Randall is a TSLA (Tesla) fan. Short selling has been a hugely controversial topic concerning Tesla over the past year, where it it was for a long time the most widely shorted stock in the US, and whose CEO had a number of very public spats with short sellers. The stock has also gone th...

- Sat Oct 27, 2018 7:24 pm UTC
- Forum: Mathematics
- Topic: Curve Filling a Rectangle
- Replies:
**21** - Views:
**10936**

### Re: Curve Filling a Rectangle

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:
**11818**

### Re: Equivalency on Mutliple Intervals

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:
**16709**

### Re: 2042: "Rolle's Theorem"

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:
**9695**

### Re: 2028: "Complex Numbers"

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:
**9695**

### Re: 2028: "Complex Numbers"

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:
**7369**

### Re: A fourth type of average?

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:
**24215**

### Re: 1989: "IMHO"

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:
**11121**

### Re: 1909:"Digital Resource Lifespan"

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:
**14948**

### 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. ...

- Fri Jul 07, 2017 8:55 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1859: "Sports Knowledge"
- Replies:
**44** - Views:
**9135**

### 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?

- Fri Jul 07, 2017 8:40 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1859: "Sports Knowledge"
- Replies:
**44** - Views:
**9135**

### 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...

- Wed Feb 08, 2017 9:14 am UTC
- Forum: Mathematics
- Topic: "There is an Exception to every rule"
- Replies:
**32** - Views:
**9199**

### 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?

- Mon Dec 26, 2016 12:29 pm UTC
- Forum: Mathematics
- Topic: Probability distribution on the power set of natural numbers?
- Replies:
**12** - Views:
**3328**

### 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

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:
**2331**

### 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...

- Sat Feb 07, 2015 2:33 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1483: "Quotative Like"
- Replies:
**83** - Views:
**15475**

### 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 &...

- Tue Nov 11, 2014 10:44 pm UTC
- Forum: Mathematics
- Topic: Congressional apportionment
- Replies:
**14** - Views:
**4666**

### 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...

- Thu Nov 06, 2014 11:36 pm UTC
- Forum: Mathematics
- Topic: how to calculate these intersections without having to write
- Replies:
**3** - Views:
**2131**

### 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.

- Thu Nov 06, 2014 11:05 pm UTC
- Forum: Mathematics
- Topic: Multiply 2 terminating numbers and get a repeating decimal?
- Replies:
**6** - Views:
**3152**

### 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...

- Wed Oct 01, 2014 8:40 pm UTC
- Forum: Mathematics
- Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
- Replies:
**42** - Views:
**11366**

### 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...

- Fri Aug 08, 2014 11:40 am UTC
- Forum: Mathematics
- Topic: is mathematics a religion?
- Replies:
**82** - Views:
**16936**

### 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...

- Sat May 31, 2014 12:46 pm UTC
- Forum: Mathematics
- Topic: hypothesis on primes
- Replies:
**9** - Views:
**4641**

### 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...

- Thu Apr 24, 2014 11:02 pm UTC
- Forum: Mathematics
- Topic: how many ways-married couples
- Replies:
**7** - Views:
**3038**

### 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...

- Fri Mar 14, 2014 5:05 am UTC
- Forum: Mathematics
- Topic: algebraic degree of sin(1 degree)
- Replies:
**4** - Views:
**2777**

### 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 ...

- Thu Feb 27, 2014 11:03 am UTC
- Forum: Mathematics
- Topic: Axiomatic mathematics has no foundation
- Replies:
**158** - Views:
**35670**

### 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.

- Thu Feb 27, 2014 10:58 am UTC
- Forum: Mathematics
- Topic: A probability(?) problem
- Replies:
**13** - Views:
**4270**

### 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 ...

- Sun Feb 23, 2014 3:03 pm UTC
- Forum: Mathematics
- Topic: A probability(?) problem
- Replies:
**13** - Views:
**4270**

### 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 ...

- Fri Feb 14, 2014 9:50 pm UTC
- Forum: Mathematics
- Topic: quarkcosh1's math coincidences thread
- Replies:
**32** - Views:
**9193**

### 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...

- Fri Feb 14, 2014 10:29 am UTC
- Forum: Mathematics
- Topic: quarkcosh1's math coincidences thread
- Replies:
**32** - Views:
**9193**

### 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 ...

- Fri Jan 24, 2014 9:40 am UTC
- Forum: Mathematics
- Topic: y = sum of subset of divisors of x
- Replies:
**2** - Views:
**2098**

### 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...

- Mon Nov 04, 2013 10:53 pm UTC
- Forum: Mathematics
- Topic: Permutations and Combinations
- Replies:
**7** - Views:
**2308**

### 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?