## Search found 671 matches

Fri Aug 30, 2013 11:42 pm UTC
Forum: Mathematics
Topic: Any usefulness of this metric?
Replies: 6
Views: 4366

### Re: Any usefulness of this metric?

It's also useful if you want to put a metric on a countable product of metric spaces.
Mon Jul 29, 2013 7:46 pm UTC
Forum: Mathematics
Topic: The physicist asks for help
Replies: 5
Views: 2043

### Re: The physicist asks for help

Standard method is to invert both sides, find t as a function of x by integrating, then take the inverse function to find x as a function of t.
Sun Jul 14, 2013 6:58 pm UTC
Forum: Mathematics
Topic: SIMPLEST PROOF OF FERMAT'S LAST THEOREM
Replies: 45
Views: 12551

### Re: SIMPLEST PROOF OF FERMAT'S LAST THEOREM

gmalivuk wrote:This is obviously not a real proof, but do other people find it interesting to point out the errors in these things?

If not, I'll stop approving them from new users.
I don't. Incoherence isn't novel, and making fun of it stops being fun once you realize that it is often caused by mental illness.
Thu Jun 13, 2013 1:43 am UTC
Forum: Computer Science
Topic: How can I know if I have talent for programming?
Replies: 21
Views: 14793

### Re: How can I know if I have talent for programming?

Sounds like you'll be fine. My first question was the only one that mattered.
Wed Jun 12, 2013 10:17 am UTC
Forum: Science
Topic: Likelihood of existence of alternate universes?
Replies: 78
Views: 17256

### Re: Likelihood of existence of alternate universes?

It's strange too since he contributed quite a bit to mathematics so he should have understood why such a claim like "I think therefore I am" just doesn't work when you examine it. According to a book I read once, Descartes only wanted to contribute to mathematics so people would take his ...
Wed Jun 12, 2013 10:02 am UTC
Forum: Computer Science
Topic: How can I know if I have talent for programming?
Replies: 21
Views: 14793

### Re: How can I know if I have talent for programming?

Do you code in your spare time? Have you tried coding in assembly? Are you willing to stick with the degree when it becomes apparent that CS, at the university level, is considered a subfield of math? How comfortable are you with discrete math, linear algebra, formal logic, and statistics? Have you ...
Fri May 31, 2013 4:09 am UTC
Forum: Science
Topic: Likelihood of existence of alternate universes?
Replies: 78
Views: 17256

### Re: Likelihood of existence of alternate universes?

Oh man, this discussion has drifted dangerously close to this story.
Fri May 31, 2013 3:04 am UTC
Forum: Mathematics
Topic: Nice proof of Euclid's Lemma?
Replies: 26
Views: 10578

### Re: Nice proof of Euclid's Lemma?

That is a clever proof! It also generalizes easily to show that the Gaussian integers and the Eisenstein integers are UFDs (instead of subtracting p_1 from q_1, subtract one of the associates of p_1 from q_1). The proof is structurally similar to the proof using the division algorithm (the main idea...
Sun May 26, 2013 9:31 am UTC
Forum: Science
Topic: Likelihood of existence of alternate universes?
Replies: 78
Views: 17256

### Re: Likelihood of existence of alternate universes?

Copper Bezel wrote:But a hypothetical universe doesn't contain any real minds, so the trick just doesn't work.
Is it bad that I burst out laughing at this sentence?

Well, my original point still stands: throwing rocks at people you disagree with is hurtful, even if they are hypothetical Platonists.
Sun May 26, 2013 7:18 am UTC
Forum: Science
Topic: Likelihood of existence of alternate universes?
Replies: 78
Views: 17256

### Re: Likelihood of existence of alternate universes?

Does 'hypothetical' now mean the same as 'completely accurately simulated in every detail'? Seeing as I didn't actually go ahead and simulate it, I'm going to say no. It was a hypothetical simulation (of a hypothetical universe (governed by hypothetical equations)). Despite the number of layers of ...
Sun May 26, 2013 6:33 am UTC
Forum: Science
Topic: Likelihood of existence of alternate universes?
Replies: 78
Views: 17256

### Re: Likelihood of existence of alternate universes?

The interpretation that is often bandied about is that a mixed state will have "separate worlds" until it is "observed". At which point people get very excited about what "observed" means. My understanding is that "observed" really just means "interacts ...
Sun May 26, 2013 5:13 am UTC
Forum: Mathematics
Topic: Nice proof of Euclid's Lemma?
Replies: 26
Views: 10578

### Re: Nice proof of Euclid's Lemma?

I don't think I've ever* seen a proof that a ring was a UFD that didn't employ the division algorithm somewhere. (Even for Dedekind domains, it might seem like you can magically prove a ring is a UFD by doing some voodoo magic (such as Minkowski's geometry of numbers or Dirichlet's class number form...
Mon May 13, 2013 8:51 am UTC
Forum: Mathematics
Topic: I suppose this is a Diophantine equation
Replies: 3
Views: 3097

### Re: I suppose this is a Diophantine equation

Ok, so we are trying to find ordered pairs of integers (a, b) that solve (for now) the equation 2a(a+1) = b^2. The first few solutions are: (0, 0), (1, 2), (8, 12), (49, 70), (288, 408) Here's a magical fact: if (a, b) is a solution, then the next largest solution is (1+3a+2b, 2+4a+3b). We can easil...
Mon Apr 08, 2013 6:17 am UTC
Forum: Mathematics
Topic: Different Way of Counting...?
Replies: 15
Views: 2590

### Re: Different Way of Counting...?

Incidentally, the collection of all people who can count on their fingers in Gray code is known* as the Gray society.

*This is the only information about the Gray society and its activities that has been made available to the public. Some speculate that it is publicized for recruiting purposes.
Wed Mar 06, 2013 5:55 am UTC
Forum: Mathematics
Topic: Discontinituous increasing function?
Replies: 20
Views: 4000

### Re: Discontinituous increasing function?

Edit: whoops, what just happened?? Edit 2: Well, while I'm here I may as well go about describing a way to construct a discontinuous function from Q to Q. First enumerate the rational numbers as q_1, q_2, ... Then start assigning rational values f_1, f_2, ... and "gap guarantees" g_1, g_2,...
Fri Mar 01, 2013 9:08 am UTC
Forum: Mathematics
Topic: Discontinituous increasing function?
Replies: 20
Views: 4000

### Re: Discontinituous increasing function?

Hint: if you have an uncountable collection of positive real numbers, you can find a finite subcollection of them with sum larger than 1. Each discontinuity gives a strictly positive jump.

Bigger hint: Wikipedia.
Sun Feb 03, 2013 11:01 am UTC
Forum: Mathematics
Topic: Irreducible ternary functions
Replies: 9
Views: 1953

### Re: Irreducible ternary functions

Here are some interesting variants: 1. Are there any partially ordered sets X and order preserving maps from X 3 to X that can't be built out of order preserving maps from X 2 to X? 2. Are there any topological spaces X and continuous maps from X 3 to X that can't be built out of continuous maps fro...
Wed Jan 16, 2013 9:50 am UTC
Forum: Logic Puzzles
Topic: Solve ALL of the Mazes [solutions]
Replies: 29
Views: 9171

### Re: Solve ALL of the Mazes [solutions]

As far as I can tell, this is only necessarily true (so far) if the steps you're taking are randomly generated for each maze. Let me see if I understand this part of the argument. First, you say that for any individual maze, if we were to take N random steps, then the chance of b not being at the g...
Tue Jan 15, 2013 2:37 pm UTC
Forum: Logic Puzzles
Topic: Solve ALL of the Mazes [solutions]
Replies: 29
Views: 9171

### Re: Solve ALL of the Mazes [solutions]

Solved the Super Hard version: There is a strategy that works! Proof: The proof is nonconstructive. Set e = 1/4^(n^2). Let N be a sufficiently large number. I claim that if you independently and randomly choose N instructions such that the probability of going up (or left) is e, and ...
Sat Dec 15, 2012 11:55 pm UTC
Forum: Mathematics
Topic: tree growth / thingy problem
Replies: 21
Views: 3202

### Re: tree growth / thingy problem

I haven’t proven it yet, but I believe the probability that the tree dies with exactly n total segments is the nth Catalan number over 4 n . So, p(1)=1/4, p(2)=2/16, p(3)=5/64, and in general p(n) = 2n!/(n!∙(n+1)!∙4 n ) = (2n choose n)/((n+1)∙4 n ). According to Mathematica, the average square root...
Sat Dec 15, 2012 1:00 am UTC
Forum: Mathematics
Topic: tree growth / thingy problem
Replies: 21
Views: 3202

### Re: tree growth / thingy problem

this seems to make sense, and the equation seems to be correct, but how did you come up with f(n) = 1/2*f(n-1) + 1/4*(1-(1-f(n-1))*(1-f(n-1))) ? There is a 1/4 chance that neither potential branch grows (leading to a probability of 0 of reaching height n if n > 1), a 1/2 chance that one potential b...
Fri Dec 14, 2012 9:25 am UTC
Forum: Mathematics
Topic: tree growth / thingy problem
Replies: 21
Views: 3202

### Re: tree growth / thingy problem

I'm not sure what you mean by the number of "steps". The average number of branches is infinity, of course: inductively, suppose we've proved the average is at least n. Then the average is at least 1 (trunk) + 2 (possible branches) * 1/2 (chance) * n (expected continuation) = 1+n. If you w...
Fri Nov 09, 2012 7:11 am UTC
Forum: Forum Games
Topic: Avoid a symbol 'twixt "d" and "f"
Replies: 249
Views: 40049

### Re: Avoid a symbol 'twixt "d" and "f"

I'm afraid I don't catch your drift. Why would it try anybody to avoid a duck? I don't mind any occasions on which avoiding ducks was at all difficult.
Fri Nov 09, 2012 6:58 am UTC
Forum: Forum Games
Topic: Avoid a symbol 'twixt "d" and "f"
Replies: 249
Views: 40049

### Re: Avoid a symbol 'twixt "d" and "f"

As I said: about as long as a duck. :P Sorry, but I find that I am at a bit of a loss - how long would you say a duck is, in plain words? It struck my imagination as an awfully particular comparison. On topic: I'm afraid of this constraint causing odd and artificial contortions in my diction. Possi...
Thu Nov 01, 2012 5:59 am UTC
Forum: Mathematics
Topic: Complex modular arithmetic
Replies: 4
Views: 3293

### Re: Complex modular arithmetic

Congratulations on getting this far. Fermat's theorem on which primes are sums of squares is really a brilliant theorem, so I don't blame you for not figuring out how to prove it on your own (my favorite proof involves the use of the analogue of Bezout's Identity for the Gaussian integers that I all...
Wed Oct 31, 2012 4:27 am UTC
Forum: Mathematics
Topic: Complex modular arithmetic
Replies: 4
Views: 3293

### Re: Complex modular arithmetic

Congratulations! You've discovered the finite field with nine elements . More generally, you can look at complex numbers of the form a+bi with a and b whole numbers, and mod out by p where p is any prime that is a multiple of 4 plus 3, to construct a finite field with p^2 elements. See if you can fi...
Fri Oct 26, 2012 4:18 am UTC
Forum: Logic Puzzles
Topic: What w/could you do with a P algorithm for factorisation?
Replies: 6
Views: 2289

### Re: What w/could you do with a P algorithm for factorisation

Anonymously publish solutions to all of the RSA factoring challenges and never tell anyone how it was done. And by anonymously I mean, go to extreme and paranoid lengths to make sure nobody ever finds out it was me. Hmm... but what happens when I see that the ante has been upped, and RSA has a new f...
Mon Oct 15, 2012 5:13 pm UTC
Forum: Science
Topic: Have you ever worked with hydrofluoric acid?
Replies: 30
Views: 13164

### Re: Have you ever worked with hydrofluoric acid?

When we worked with this stuff we were just told to immediately wash it off and calmly freak out if we spilled some on ourselves. I suppose a calcium gel makes sense though.

Also, I wouldn't recommend drinking it. It's very bad for your teeth.
Sun Sep 30, 2012 8:50 am UTC
Forum: Gaming
Topic: Go, and the rule of it.
Replies: 11
Views: 2383

### Re: Go, and the rule of it.

Suddenly I doubt that you have ever actually played go...
Fri Sep 28, 2012 4:45 am UTC
Forum: Gaming
Topic: Go, and the rule of it.
Replies: 11
Views: 2383

### Re: Go, and the rule of it.

In order to make this game look like go, you need to add one more rule: 6. Instead of placing a piece, a player may return a piece he had previously captured to his opponent. (Additionally, the players keep track of captured enemy pieces.) This way players get one free move at the end of the game (p...
Sun Sep 02, 2012 2:24 am UTC
Forum: Comics/Graphic Novels
Replies: 687
Views: 192714

Was I the only one who couldn't get the game to play at all? I got the intro, but it just kept looping indefinitely. I thought that was the whole update until I saw this thread... (I'm running Firefox on Ubuntu.)
Sat Aug 25, 2012 9:56 am UTC
Forum: Fictional Science
Topic: Perpetual light
Replies: 2
Views: 2723

### Re: Perpetual light

poxic wrote:First you need a perpetual source of moths.
I don't think you've ever had a moth infestation.
Sat Aug 25, 2012 9:32 am UTC
Forum: Logic Puzzles
Topic: Troll Science: Pi
Replies: 45
Views: 26553

### Re: Troll Science: Pi

On the other hand, how did ancient mathematicians estimate the value of pi? By constructing inscribed and circumscribed polygons and computing their perimeters. How come this limit works, but the original one doesn't? Because the inscribed and circumscribed polygons have tangent directions approach...
Wed Aug 22, 2012 4:30 am UTC
Forum: Religious Wars
Topic: Plural of "Octopus"
Replies: 89
Views: 64397

### Re: Plural of "Octopus"

I have always maintained that the correct pluralization is "octopoxen".
Tue Aug 21, 2012 11:43 pm UTC
Forum: Mathematics
Topic: The saga goes on - Viglen's number incompetency, part three
Replies: 38
Views: 5116

### Re: The saga goes on - Viglen's number incompetency, part th

It's related intuition, not strictly required. My approach is an alternate way to characterize the problem. A prime p satisfies your condition if and only if 2 is not a primitive root mod p. This is false.... very false... For example, 2 is not a primitive root mod 43 (since 2 is a cube mod 43), bu...
Tue Aug 21, 2012 1:40 am UTC
Forum: Mathematics
Topic: The saga goes on - Viglen's number incompetency, part three
Replies: 38
Views: 5116

### Re: The saga goes on - Viglen's number incompetency, part th

As implied by fishfry, it appears that the general problem might be open? Viglen's question is not open. For odd primes p, 2^((p-1)/2) is congruent to 1 mod p exactly when 2 is congruent to a square mod p (one direction is easy: if 2 is congruent to x^2, then 2^((p-1)/2) is congruent x^(p-1), and b...
Sat Aug 11, 2012 7:55 am UTC
Forum: Mathematics
Topic: Collatz conjecture
Replies: 11
Views: 3002

### Re: Collatz conjecture

Ok, good. If we blindly apply the results stated in http://en.wikipedia.org/wiki/Linear_forms_in_logarithms as a blackbox, we can see that log((m+n)log(2) - nlog(3)) > -18*3!*2^3*32^4*log(4)^3*log(m+n) > -3*10^9*log(m+n), so m+n - log 2 (3)n > (m+n) -3*10^9 /log(2), and for large enough m and n this...
Fri Aug 10, 2012 6:58 pm UTC
Forum: Mathematics
Topic: Collatz conjecture
Replies: 11
Views: 3002

### Re: Collatz conjecture

oh, hold on. For some reason I was assuming that you had proven that m+n-log2(3)n was also positive. If you don't have that, you can't do anything....
Thu Aug 09, 2012 5:45 am UTC
Forum: Mathematics
Topic: Collatz conjecture
Replies: 11
Views: 3002

### Re: Collatz conjecture

For anyone who has not heard of the collatz conjecture before, the collatz conjecture states that if you take any number, and if it is even, divide by 2, and if it is odd, multiply by three, add 1, then divide by two, and if you repeat this procedure long enough, eventually any positive integer wil...
Thu Jun 21, 2012 12:40 am UTC
Forum: Mathematics
Topic: Stuck on an easy-looking combinatorial problem
Replies: 3
Views: 1042

### Re: Stuck on an easy-looking combinatorial problem

This isn't so bad if you induct on the size of the set - for the induction to go through, you just need to check that the sum of the n largest multiplicities is at most 0 + 1 + ... + (n-1), since when a multiplicity of k increases to a multiplicity of k+1, the sum of the squares of the ...

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