Search found 798 matches

by MartianInvader
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.
by MartianInvader
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...
by MartianInvader
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 :D
by MartianInvader
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 :lol: )
by MartianInvader
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...
by MartianInvader
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.
by MartianInvader
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...
by MartianInvader
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 ...
by MartianInvader
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 ...
by MartianInvader
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. :oops:
by MartianInvader
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)(ey)2 - (1/2) = xey

(1/2)(ey)2 - xey - (1/2) = 0

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.
by MartianInvader
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:
I was actually thiking of "You won't give me $10, nor will you give me a million dollars", but of course yours is just as good if not better.
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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 ...
by MartianInvader
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 ...
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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.
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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").
by MartianInvader
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/...
by MartianInvader
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...
by MartianInvader
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?
by MartianInvader
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,...
by MartianInvader
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!
by MartianInvader
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, ...
by MartianInvader
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
by MartianInvader
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:
4. The types of US currency, from a penny to the $1000.00 bill? Including the golden dollar, so there's 12 faces even with the repeats of Washington and Lincoln.
by MartianInvader
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...
by MartianInvader
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...
by MartianInvader
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.
by MartianInvader
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 ...

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