## Search found 798 matches

- Wed Dec 12, 2007 5:51 pm UTC
- Forum: Mathematics
- Topic: Discrete probability distributions on dense sets
- Replies:
**9** - Views:
**1821**

### Re: Discrete probability distributions on dense sets

I'm not sure, but here's a similar-themed cool thing: One can construct an open subset of the reals which contains every rational number but has finite (actually, arbitrarily small) measure.

- Mon Dec 10, 2007 11:33 pm UTC
- Forum: Mathematics
- Topic: Numberline?
- Replies:
**22** - Views:
**3077**

### Re: Numberline?

I just wanted to add that there's higher-dimensional analogues of both the real projective line jestingrabbit mentioned, and of the Riemann sphere explained by codemaster. This is the concept of projective space , particularly real projective space and complex projective space . For example, in dime...

- Mon Dec 03, 2007 3:57 am UTC
- Forum: Mathematics
- Topic: Distance from Sqrt(x) to .5x
- Replies:
**9** - Views:
**1879**

### Re: Distance from Sqrt(x) to .5x

We were talking about which integers x give integer results. And when the square root of an integer isn't an integer, it's irrational.

By the way, I went to UC Berkeley, so if your username is any indication of your abilities, I can slow down and explain it with shorter words

By the way, I went to UC Berkeley, so if your username is any indication of your abilities, I can slow down and explain it with shorter words

- Sun Dec 02, 2007 4:24 pm UTC
- Forum: Mathematics
- Topic: Distance from Sqrt(x) to .5x
- Replies:
**9** - Views:
**1879**

### Re: Distance from Sqrt(x) to .5x

It doesn't take much more to prove it - sqrt(x) is irrational if its not an integer, and x/2 is always rational, so if they're both not integers the difference will be irrational, hence not an integer. (If one's an integer and the other's not, the proof is left as an excercise )

- Thu Nov 29, 2007 6:55 pm UTC
- Forum: Mathematics
- Topic: Favourite Field of Math?
- Replies:
**60** - Views:
**5249**

### Re: Favourite Field of Math?

To btilly and Kalak_z: I've never seen anything more powerful than Euler characteristic used in graph theory, and Euler characteristic is, what? 200 years old? It's a really elementary piece of algebraic topology. If you take an algebraic topology class out of Allen Hatcher's book, there is an exerc...

- Wed Nov 28, 2007 2:09 am UTC
- Forum: Logic Puzzles
- Topic: DC101's "Where in the World"
- Replies:
**48** - Views:
**5725**

### Re: DC101's "Where in the World"

How shock-y is this particular show? Could be the cell of some Guantanamo prisoner who's been in the news recently or something.

- Wed Nov 28, 2007 2:02 am UTC
- Forum: Mathematics
- Topic: Imaginary negative
- Replies:
**17** - Views:
**3612**

### Re: Imaginary negative

f(z) = conj(z) is sort of differentiable. Viewed as a function from the plane to itself, it's differentiable in that it has directional derivatives (its derivative is 1 in the positive real direction, -1 in the positive imaginary direction). But it's not complex differentiable, in the sense that lim...

- Mon Nov 26, 2007 12:09 am UTC
- Forum: General
- Topic: Prove You Are Real
- Replies:
**167** - Views:
**14812**

### Re: Prove You Are Real

I'm real: I am me. I have brown hair. Imagine what I look like. Now you've thought about what I am. Something made you think about that, and I am that something. I may not be human, I may be nothing more than some trick of your own mind, but nonetheless, you know I am something because I interacted ...

- Sun Nov 25, 2007 10:50 pm UTC
- Forum: Serious Business
- Topic: Future Historians
- Replies:
**15** - Views:
**3462**

### Re: Future Historians

I think there's SO much information being recorded that there will be plenty available for study, even if 99% of it gets lost 1000 years from now. So studying anything that's happening now will be like studying well-documented events of 1000 years ago: Plenty of info, the main challenge is figuring ...

- Sun Nov 25, 2007 6:26 pm UTC
- Forum: Mathematics
- Topic: How would I solve for y in this equation?
- Replies:
**8** - Views:
**1451**

### Re: How would I solve for y in this equation?

Aradae wrote:where'd the 1/4 come from?

Erm, eh, hmm, what 1/4? Clearly the first coefficient is 1/2.

- Sun Nov 25, 2007 6:16 pm UTC
- Forum: Mathematics
- Topic: How would I solve for y in this equation?
- Replies:
**8** - Views:
**1451**

### Re: How would I solve for y in this equation?

simplifying the log of a difference is pretty tough. I'd go with:

(1/2)(e

(1/2)(e

Use the quadratic formula with a = 1/2, b = -x and c = -1/2 to get an equation for e^y in terms of x. Then take the natural log of that and you're done.

(1/2)(e

^{y})^{2}- (1/2) = xe^{y}(1/2)(e

^{y})^{2}- xe^{y}- (1/2) = 0Use the quadratic formula with a = 1/2, b = -x and c = -1/2 to get an equation for e^y in terms of x. Then take the natural log of that and you're done.

- Sun Nov 25, 2007 3:42 pm UTC
- Forum: Logic Puzzles
- Topic: Money and fruit
- Replies:
**27** - Views:
**3096**

### Re: Money and fruit

Avin's got the first one.

**Spoiler:**

- Sun Nov 25, 2007 1:46 am UTC
- Forum: Logic Puzzles
- Topic: Money and fruit
- Replies:
**27** - Views:
**3096**

### Re: Money and fruit

4=5: For the first question, You're assuming the amount of money will be chosen in some uniform random way, of which you have no guarantee. Perhaps I could phrase the question another way: a) Which of the two offer-giving gentlemen would you rather BE, and b) Why is the answer to questio...

- Sun Nov 25, 2007 1:21 am UTC
- Forum: Mathematics
- Topic: Some Vector Questions
- Replies:
**6** - Views:
**1459**

### Re: Some Vector Questions

Hope these help: 1. A system with a parametic solution does have infinitely many solutions; each solution represents a point (from what I gather, probably a point in 3-dimensional space in your case). A line has infinitely many points, so it makes sense to write it in a parametric way (typically som...

- Sat Nov 24, 2007 11:23 pm UTC
- Forum: Logic Puzzles
- Topic: Money and fruit
- Replies:
**27** - Views:
**3096**

### Money and fruit

Here's two puzzles, in case one has been posted before (sorry if it has!) Puzzle 1 - There's a gentleman on your right who makes you the following offer - you shall make any statement. If it's true, he will give you $10. If it's false, he will give you some amount of money OTHER than $10 (perhaps mo...

- Sat Nov 24, 2007 10:22 pm UTC
- Forum: Logic Puzzles
- Topic: Left/Right
- Replies:
**38** - Views:
**4131**

### Re: Left/Right

The problem with your question, is that you said "bits of data" instead of the original question, which assumed we used radios. The original question didn't allow for pictures. This one does. Therefore, the concept of left and right can be declared, even if they reverse it. I think by &qu...

- Sat Nov 24, 2007 10:09 pm UTC
- Forum: Logic Puzzles
- Topic: Bears
- Replies:
**6** - Views:
**2228**

### Re: Bears

I'm really confused about what the logician is and isn't allowed to do here. Can he just shine a flashlight on them? Can he get close up to them? Touch them? Can he throw stones at them? Does he get eaten if the bears see/hear/smell him? Can he navigate his way through this pitch-black darkness with...

- Sat Nov 24, 2007 5:26 pm UTC
- Forum: Mathematics
- Topic: What math should I move on to?
- Replies:
**27** - Views:
**3358**

### Re: What math should I move on to?

I didn't really "get" proofs until I took an abstract algebra class my second year of college. When it comes to understanding what math logic is all about, I think abstract algebra is the best way to learn. Introductory math logic /set theory courses tend to ask for such easy proofs you do...

- Fri Nov 16, 2007 9:09 pm UTC
- Forum: Mathematics
- Topic: Can you make a probability graph from a function?
- Replies:
**10** - Views:
**1858**

### Re: Can you make a probability graph from a function?

Well, I'm not sure exactly how you've defined "prbability density", but from what I can tell from your description and examples, it sounds like you're looking at the derivative of the inverse function, normalized so that its integral is 1. That is to say, you want to look at values in the ...

- Fri Nov 16, 2007 2:53 pm UTC
- Forum: Mathematics
- Topic: Can I get an example of this?
- Replies:
**5** - Views:
**1112**

### Re: Can I get an example of this?

It's been a while, so correct me if I'm wrong, but I'm pretty sure point-masses don't have continuous distributions associated to them, and that's the whole reason one defines a concept of "distribution" instead of just "integration against a smooth function." A point mass would ...

- Mon Nov 12, 2007 4:59 am UTC
- Forum: Mathematics
- Topic: Pythagorean Proofs
- Replies:
**24** - Views:
**3078**

### Re: Pythagorean Proofs

Ok, sorry, misread that proof. Nonetheless, I still think you could approach this problem... how about a partial order? P <= P' if P can be obtained from P' by successive removals of useless steps (maybe allow some other types of one-way changes as well). Then you'd turn the set of all proofs into a...

- Sun Nov 11, 2007 4:44 pm UTC
- Forum: Mathematics
- Topic: Pythagorean Proofs
- Replies:
**24** - Views:
**3078**

### Re: Pythagorean Proofs

I think you probably could define a good equivalence (or something similar) so that there might be a finite number of proofs. For example, the first thing I would do is say that if we have a statement in a proof that is never used later (e.g. an unneccessary '1+1=2'), then we can delete that stateme...

- Sun Nov 11, 2007 4:18 pm UTC
- Forum: Mathematics
- Topic: weird question
- Replies:
**25** - Views:
**2920**

### Re: weird questin

I must admit, my least favorite part of math is differential equations.

- Sat Nov 10, 2007 12:01 am UTC
- Forum: Logic Puzzles
- Topic: Helpful and Unhelpful (Solution thread)
- Replies:
**30** - Views:
**3919**

### Re: Helpful and Unhelpful (Solution thread)

I doubt that its provably impossible to figure out which door to go through, due to the not-well-defined nature of the word "Helpful". It seems you'd go in circles (Unhelpful will act just like Helpful, which means Helpful would act differently to distinguish himself, which means Unhelpful...

- Sun Nov 04, 2007 9:22 pm UTC
- Forum: Mathematics
- Topic: Using Logs to Solve
- Replies:
**6** - Views:
**1368**

### Re: Using Logs to Solve

xlog(x)=log(x) x=1 Technically you can't even quite do this, since when you divide by log(x) you're assuming x isn't 1 (otherwise you're dividing by zero). So this actually shows a contradiction and proves that x can't be any positive number OTHER than 1, which you can then plug in and find that it...

- Sun Nov 04, 2007 3:29 am UTC
- Forum: Mathematics
- Topic: Pi repeats and the uncountable infinite set of numbers...
- Replies:
**14** - Views:
**2195**

### Re: Pi repeats and the uncountable infinite set of numbers...

SimonM wrote:Depends on whether or not the digits are perfectly randomly distributed

It's an open question as to whether they are, but the first 10 trillion or so (all we've calculated) seem to be (assuming you're using a reasonable definition of "random").

- Fri Nov 02, 2007 2:20 pm UTC
- Forum: Mathematics
- Topic: 2=1
- Replies:
**11** - Views:
**1814**

### Re: 2=1

Not sure if it's been done before so I'll just tack it onto this thread: 16 - 36 = 25 - 45----------------------------(Both are -20) 16 - 36 + 81/4 = 25 - 45 + 81/4----------(add 81/4 to each side) (4 - 9/2)^2 = (5 - 9/2)^2------------------(simplify the x^2 + 2xy + y^2 expressions) 4 - 9/2 = 5 - 9/...

- Fri Nov 02, 2007 1:55 pm UTC
- Forum: Mathematics
- Topic: Geodesics: Donuts are Delicious
- Replies:
**10** - Views:
**1733**

### Re: Geodesics: Donuts are Delicious

Well, it depends what sort of metric you have on the torus, but I'll assume it's the standard one you get from identifying the sides of a square with sidelength 1. Try drawing 9 copies of this sqaure in a 3x3 pattern, and put your first point in the middle square. Now you can put 9 copies of your se...

- Wed Oct 31, 2007 9:27 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2548**

### Re: City Planning

Token wrote:Given that it was big enough to scare him into running an entire kilometer, I assume it was the penguin queen, who resides exactly at the South Pole.

Ah, but if it was the penguin queen at the South Pole, then he didn't run at all, now, did he?

- Wed Oct 31, 2007 2:01 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2548**

### Re: City Planning

Ok, I've changed the statement of the problem to be a bit less obvious. If anyone's curious, the math concept that inspired this was that of a Cayley Graph (wikipedia has a nice writeup on what these are). The problem is actually asking you to find the Cayley graph of the group with presentation <a,...

- Wed Oct 31, 2007 12:13 am UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2548**

### Re: City Planning

Indeed. Hm, 3 answers in 15 minutes... I guess it was too easy with the sports thing, maybe I should have just left out the 4th condition and instead asked what familiar graph the streets make.

Anyhoo, well done!

Anyhoo, well done!

- Tue Oct 30, 2007 11:53 pm UTC
- Forum: Logic Puzzles
- Topic: City Planning
- Replies:
**19** - Views:
**2548**

### City Planning

Here's a puzzle inspired by (though not requiring) some rather hefty mathematics: A city planner is given some odd requirements by a rather eccentric governor for the city he's designing. There are 4 requirements: - Each street corner must have exactly 3 streets (not the usual 4). Of these streets, ...

- Tue Oct 30, 2007 10:06 pm UTC
- Forum: Forum Games
- Topic: Count to 1 1000 times!
- Replies:
**1000** - Views:
**161641**

### Re: Count to 1 1000 times!

16836 rewritten in base 26

- Tue Oct 30, 2007 8:11 pm UTC
- Forum: Logic Puzzles
- Topic: 10 Word Puzzles
- Replies:
**17** - Views:
**3289**

### Re: 10 Word Puzzles

Guess for 4.

**Spoiler:**

- Mon Oct 29, 2007 9:32 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**4280**

### Re: Circles on a plane

I'm not certain, but it seems to me that if you're talking about open circles, then the fractal-ish pattern would leave out points, but if you're talking about closed circles, then everything gets covered. Neither was specified at the start of the problem, so I was using closed circles. quintopia: Y...

- Sun Oct 28, 2007 11:58 pm UTC
- Forum: Mathematics
- Topic: limit of a function defined in terms of another function
- Replies:
**18** - Views:
**2109**

### Re: limit of a function defined in terms of another function

Can't you interpolate a quadratic onto any 3 points? In particular, I think if you find the quadratic passing through (0, .5), (.5, .8 ), and (.8, .5), you'll get a quadratic function which satisfies the given conditions, but repeated applications of the function will keep oscillating between .5 and...

- Sat Oct 27, 2007 6:21 pm UTC
- Forum: General
- Topic: INTRO THREAD THE THIRD
- Replies:
**10920** - Views:
**2278820**

### Re: POST HERE FIRST - INTRO THREAD THE THIRD

Hi, I'm a math grad student in the US. Stumbled onto xkcd a while ago and loved it (I really identified with a lot of the comics in the archives). I really liked the math and logic puzzles parts of these forums, and finally got around to registering today.

- Sat Oct 27, 2007 6:12 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**4280**

### Re: Circles on a plane

I had to register just to comment on this. You never said all the circles had to be the same size. If they can get very small, you can cover the plane with a fractal-like pattern of circles so that each circle intersects only four others, and each point of the plane is contained in no more than two ...