Search found 67 matches

by bray
Fri Nov 06, 2009 5:13 pm UTC
Forum: Mathematics
Topic: "I'm thinking of a number..." game in a group
Replies: 13
Views: 2562

Re: "I'm thinking of a number..." game in a group

That doesn't mean it can't be solved. It just means we need to figure out what we mean by "optimal play". In particular, I think it should mean that players act to maximize their expected chance of winning, choosing randomly among the options available to them that do so (given that the ot...
by bray
Tue Nov 03, 2009 11:56 pm UTC
Forum: Mathematics
Topic: "I'm thinking of a number..." game in a group
Replies: 13
Views: 2562

Re: "I'm thinking of a number..." game in a group

Why would the first player choose to play N/2 when they know that it will result in a 1/N chance of winning? Playing 2 would give them at least 2/N.
by bray
Tue Nov 03, 2009 11:20 pm UTC
Forum: Mathematics
Topic: "I'm thinking of a number..." game in a group
Replies: 13
Views: 2562

Re: "I'm thinking of a number..." game in a group

For two players, the game is actually biased in favor of the first guesser. If the two players play optimally and are guessing between 1 and N, then when N is even, one will choose N/2 and the other will choose N/2 + 1 and both will have an equal chance of winning. If N is odd, though, then the firs...
by bray
Tue Aug 25, 2009 11:36 pm UTC
Forum: Mathematics
Topic: Question on Gram-Schmidt Process.
Replies: 7
Views: 1203

Re: Question on Gram-Schmidt Process.

Do you not have a book? Or access to Wikipedia?
by bray
Fri Aug 14, 2009 5:25 pm UTC
Forum: Mathematics
Topic: Signed Measure Clarification
Replies: 2
Views: 704

Re: Signed Measure Clarification

Well, if you use the wikipedia definition then I think it follows that in any signed measure space you just can't find a sequence of sets whose measures are conditionally convergent. So no problem! That seems...pretty wrong though. I think your requirement that having a conditionally convergent deco...
by bray
Wed Jul 15, 2009 4:37 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0610: "Sheeple"
Replies: 511
Views: 99649

Re: "Sheeple" Discussion

If you're not actively checking yourself against whim, instant gratification, etc, and just assuming that what you want = what's best for your life, you will obviously run in to these problems. This is all part of what is necessary to being rationally self-interested. Best for your life? What does ...
by bray
Thu May 28, 2009 2:59 pm UTC
Forum: Mathematics
Topic: Recommended resources for teaching oneself Alg II?
Replies: 4
Views: 1151

Re: Recommended resources for teaching oneself Alg II?

I wouldn't worry about bothering your teachers. As long as you don't act like an arrogant smartass (which sounds unlikely based on your post), they'll probably be thrilled to find a student who's actually eager to learn. As for books, I'm not really sure. If you can get your hands on a copy of the b...
by bray
Thu May 28, 2009 2:25 pm UTC
Forum: Mathematics
Topic: What's in a number?
Replies: 74
Views: 5927

Re: What's in a number?

The claim that definitions should be stated as "if and only if" has always struck me as confused. A definition is not a logical argument. It's...a definition. If you're not happy with, "A set with a binary operation is a group if blah blah blah" don't make it "if and only if...
by bray
Thu May 28, 2009 2:17 pm UTC
Forum: Mathematics
Topic: Hypothesis testing
Replies: 8
Views: 1129

Re: Hypothesis testing

There's no need to bring normal approximations into this. You can just calculate the exact tail probability directly.
by bray
Thu May 14, 2009 4:58 pm UTC
Forum: Mathematics
Topic: Submitting a paper
Replies: 14
Views: 1705

Re: Submitting a paper

Maybe "I'd ask the student to bring me back a list and help them decide how to rank them." is what you originally meant but to me, at least, it sounds quite different from "Good job. Now find a place to publish it."
by bray
Wed May 13, 2009 9:36 pm UTC
Forum: Mathematics
Topic: Submitting a paper
Replies: 14
Views: 1705

Re: Submitting a paper

Indeed, and noting that a paper is of the quality to be published and encouraging the advisee to publish it is doing exactly that: "advising." However, the point of advising someone is to prepare them to become an independent academic. One thing one needs to learn for that purpose is how ...
by bray
Wed May 13, 2009 9:19 pm UTC
Forum: Mathematics
Topic: Computer Random Number Generator - How?
Replies: 23
Views: 2186

Re: Computer Random Number Generator - How?

I think the problem with that scheme is more apparent if you work in base two (where you should probably be working anyway). When used to generate n digit (i.e. bit) numbers, it can only produce n different numbers. And those numbers are independent of your seed value. It probably becomes less bad a...
by bray
Wed May 13, 2009 9:04 pm UTC
Forum: Mathematics
Topic: Ridiculously simple probability question
Replies: 18
Views: 1372

Re: Ridiculously simple probability question

Juuh, I got them to change their minds. They charged 1,50 instead of 1 euro. They had 40 pies and made about 80 euro profit. :P Err... So if you run the game by having 40 pies and having people play until the pies run out, then the total number of games played will be 40 + X where X has a negative ...
by bray
Tue May 12, 2009 10:10 pm UTC
Forum: Mathematics
Topic: Ridiculously simple probability question
Replies: 18
Views: 1372

Re: Ridiculously simple probability question

What Ended said about the probabilities involved. Though the expected profit per game is going to be 0.42*(1 - 3) + (1-0.42)*1 = -0.26. Beyond that though, there's the question of how surprising a result turning a profit would be. To break even we have to have at least twice as many losses as wins a...
by bray
Tue May 12, 2009 9:31 pm UTC
Forum: Mathematics
Topic: Submitting a paper
Replies: 14
Views: 1705

Re: Submitting a paper

quintopia wrote:If I were the advisor, I would have said "Good job. Now find a place to publish it."


The job of an advisor is to advise. I fail to see why this would apply to the publication process any less than anything else.
by bray
Tue May 12, 2009 5:32 pm UTC
Forum: Mathematics
Topic: Submitting a paper
Replies: 14
Views: 1705

Re: Submitting a paper

If this was done during a REU program, don't you have a faculty advisor that you can (and probably should) discuss this with?
by bray
Sat Apr 18, 2009 12:31 pm UTC
Forum: Mathematics
Topic: A Couple (easy?) Questions
Replies: 5
Views: 899

Re: A Couple (easy?) Questions

In general, it's the students job to actually *say* what logic they're using, so that the person grading can spend their time grading rather than on attempts at mind-reading. But of course, yes, you do have to do some mind reading sometime. But my mind-reading here didn't lead me to that conclusion....
by bray
Sat Apr 18, 2009 10:45 am UTC
Forum: Mathematics
Topic: A Couple (easy?) Questions
Replies: 5
Views: 899

Re: A Couple (easy?) Questions

I wouldn't describe the reasoning for b as correct either. Just showing that you don't get the origin for two values of (a,b,c) doesn't show that you don't get it for any value of (a,b,c).
by bray
Thu Apr 16, 2009 6:24 pm UTC
Forum: Mathematics
Topic: Number of subsets of bounded size.
Replies: 10
Views: 1283

Re: Number of subsets of bounded size.

I think that first approximation is not going to get you anywhere good. If we consider the quantity \sum_{k = 0}^{\sqrt{8n}} \frac{n^k}{k!} to be the \sqrt{8n} th Taylor approximation to e^n , then we get that this is equal to e^n - R_{\sqrt{8n}}(n) . Unless I screwed up somewhere, maximizin...
by bray
Thu Apr 16, 2009 3:57 pm UTC
Forum: Mathematics
Topic: Singularics - Claims to prove RH by dividing by 0
Replies: 21
Views: 3540

Re: Singularics - Claims to prove RH by dividing by 0

Even if we were to accept that this was the work of a troll, the trollery would be so extensive as to be basically indistinguishable from mental illness. Mentally ill people exist and the chances of some random person on the internet being able to argue them out of their delusions is just about zero...
by bray
Fri Apr 03, 2009 3:24 pm UTC
Forum: Mathematics
Topic: Function extrema in general
Replies: 9
Views: 1614

Re: Function extrema in general

I think what Yesila was going for is "f(x) is on the boundary of f(V)".
by bray
Thu Apr 02, 2009 2:33 pm UTC
Forum: Mathematics
Topic: Measure theory problem - test preparation.
Replies: 10
Views: 1535

Re: Measure theory problem - test preparation.

Yeah, getting that 1/2 wasn't really necessary. It just seemed...right, though.
by bray
Thu Apr 02, 2009 7:39 am UTC
Forum: Mathematics
Topic: Measure theory problem - test preparation.
Replies: 10
Views: 1535

Re: Measure theory problem - test preparation.

After thinking about this for a long time and writing up my solution, I reread and realized that I've come up with what I believe is the same solution as demon. As you say, Yakk, things took a strange left turn near the end of demon's last post, but I think this is (a slightly stronger version) of w...
by bray
Fri Mar 27, 2009 10:21 pm UTC
Forum: Mathematics
Topic: Another Summation Question
Replies: 7
Views: 863

Re: Another Summation Question

And it wasn't even one of those ten-minutes-later "ninja'd"s. Still, I clearly am the winner.
by bray
Fri Mar 27, 2009 10:10 pm UTC
Forum: Mathematics
Topic: Another Summation Question
Replies: 7
Views: 863

Re: Another Summation Question

Yeah, given that someone's teaching the class, I think you can assume that they tried the ratio test. I think you actually don't need any test at all (well, if you assume a certain well known series diverges):
Spoiler:
[math]2^{1/n} - 1 = e^{ln(2)/n} - 1 \geq \frac{\ln(2)}{n}[/math]
by bray
Mon Mar 23, 2009 9:57 pm UTC
Forum: Mathematics
Topic: Definition of a gaussian stochastic process
Replies: 6
Views: 1002

Re: Definition of a gaussian stochastic process

but the multivariate normal condition is stronger than that - it says that every finite linear combination of the X t must be normally distributed. And yes, a multivariate normal distribution does not require that its components be independent. The given definition makes no mention of linear combin...
by bray
Fri Mar 20, 2009 9:58 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0558: "1000 Times"
Replies: 266
Views: 49755

Re: "1000 Times" discussion

Please refrain from speaking about this subject until you have, at the very least, read the Wikipedia article on Keynesian economics. Virtually no one who actually studies how economies work thinks that what you're saying makes any sense. Just to be clear: not everyone agrees with Keynesian economi...
by bray
Fri Mar 20, 2009 9:39 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0558: "1000 Times"
Replies: 266
Views: 49755

Re: "1000 Times" discussion

I read somewhere that for every $1,000,000,000 spent by government, that's about $8 out of YOUR pocket. Well, if you read it somewhere, it must be true. If you take $1,000,000,000 and divide it by the number of taxpayers (138 million), then you get roughly $7.25 which I can only imagine is where th...
by bray
Sat Mar 14, 2009 7:04 pm UTC
Forum: Mathematics
Topic: The Chow&Robbins problem
Replies: 19
Views: 2079

Re: The Chow&Robbins problem

Here's kind of a meta-question: can the optimal strategy be expressed (as, I think, the linked article implicitly assumes) by a function h(t) where you stop if your string has t tails and at least h(t) heads? My intuition says a very strong yes but it's not clear to me how to prove it. Absolutely. ...
by bray
Sat Mar 14, 2009 6:47 pm UTC
Forum: Mathematics
Topic: The Chow&Robbins problem
Replies: 19
Views: 2079

Re: The Chow&Robbins problem

antonfire wrote:
bray wrote:Eventually you're sure to get to 0.5 + epsilon.

No, you're not. You're sure to get above 0.5, but given epsilon>0, there is no guarantee that you will ever get to 0.5+epsilon.


Yes, I was being loose in my language. I just meant, "You'll get to something strictly greater than 0.5"
by bray
Sat Mar 14, 2009 6:20 pm UTC
Forum: Mathematics
Topic: The Chow&Robbins problem
Replies: 19
Views: 2079

Re: The Chow&Robbins problem

So it seems any strategy that has an ending condition with 50% heads and 50% tails can certainly be improved. I guess you don't need such an ending condition to exist, but I'd at least call this strong evidence. 50/50 is a very special condition in this game, though. Namely, it's one that you can b...
by bray
Fri Mar 13, 2009 9:32 pm UTC
Forum: Mathematics
Topic: What is wrong with this differentiation?
Replies: 19
Views: 2861

Re: What is wrong with this differentiation?

That definition is fine, I guess, but it's not clear to me what the point is. Yes, it reduces to normal summation when both limits of summation are integers, but so would an infinite number of other definitions. It does have the advantage over some other possible definitions that it turns the nonsen...
by bray
Fri Mar 13, 2009 3:58 pm UTC
Forum: Mathematics
Topic: What is wrong with this differentiation?
Replies: 19
Views: 2861

Re: What is wrong with this differentiation?

Set x equal to any positive rational number, and define: \sum\limits_{i=1}^{a+b/c} f(x)+ =\sum\limits_{i=1}^{a} f(x)+f(x)\frac{b}{c} This only defines the sum when what you're summing is constant. And so it doesn't apply to any of the examples you gave. I'm assuming what you...
by bray
Tue Mar 03, 2009 6:29 pm UTC
Forum: Mathematics
Topic: Augmented matrix
Replies: 12
Views: 1605

Re: Augmented matrix

So what, in particular, have you tried?
by bray
Mon Feb 16, 2009 8:38 am UTC
Forum: Mathematics
Topic: The probability of impossible
Replies: 63
Views: 7536

Re: The probability of impossible

codyhotel wrote:Get it?


For future reference, the phrase "Get it?" is almost always going to just annoy whomever you're talking to. All the more so if what you've said immediately preceding it didn't actually make any sense.
by bray
Fri Feb 13, 2009 3:37 pm UTC
Forum: Mathematics
Topic: The probability of impossible
Replies: 63
Views: 7536

Re: The probability of impossible

Even in describing it as an ideal dartboard, which I get, you still have a dart with an obviously non-zero area tip. Err...why? Assuming we're not throwing a non-ideal dart at our ideal dartboard, why wouldn't the dart have a tip that's a point? (And even if you chose not to for some reason, you co...
by bray
Tue Feb 03, 2009 5:06 pm UTC
Forum: Mathematics
Topic: Number Theory Problem(s)
Replies: 8
Views: 1132

Re: Number Theory Problem(s)

I was about to claim that I had a third solution when I decided maybe I should check what Bertrand's postulate (which from now on I will call the Chebyshev-Bertrand theorem) was. I had forgotten that that thing had a name and assumed it was just a piece of folklore. The power of 2 solution is much m...
by bray
Tue Feb 03, 2009 4:55 pm UTC
Forum: Mathematics
Topic: x - cos(x) = 0
Replies: 36
Views: 11291

Re: x - cos(x) = 0

Why? With enough digits it's trivial to compute the continued fraction representation of the Dottie number up to some desired accuracy and get good rational approximations. It's not a very useful exercise on a number that isn't known to have any nice algebraic properties. Because it's there. And, y...
by bray
Tue Feb 03, 2009 4:49 pm UTC
Forum: Mathematics
Topic: Where'd I make my mistake? [Line integrals]
Replies: 5
Views: 1036

Re: Where'd I make my mistake? [Line integrals]

Man, seriously, what the hell. I should not do these things first thing after waking up. I have no idea what I was talking about since this is obviously not a complex analysis type line integral. My brain obviously just went, "Line integral. Zero. Cauchy's theorem." There's still a simple ...
by bray
Tue Feb 03, 2009 3:02 pm UTC
Forum: Mathematics
Topic: Where'd I make my mistake? [Line integrals]
Replies: 5
Views: 1036

Re: Where'd I make my mistake? [Line integrals]

If you closed up your curve by including the segment along the y-axis then Cauchy's integral formula would tell you that the integral around that closed curve is zero. But your function is identically zero on that extra segment so the integral along the curve you're giving must also be zero.

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