Search found 209 matches

by aguacate
Wed Aug 15, 2007 10:56 pm UTC
Forum: Mathematics
Topic: Help with this theorem - accumulation pts and cpt sets
Replies: 11
Views: 2573

Help with this theorem - accumulation pts and cpt sets

Just learning about compactness so please bear with me THEOREM Let S* denote the accumulation points of S. Assume: 1) K is compact 2) S is a subset of K 3) S is infinite Then: S* intersect K is not empty I understand the proof of this, but what I don't understand is why bother with S* intersect K? A...
by aguacate
Wed Aug 15, 2007 10:39 pm UTC
Forum: Science
Topic: Synchronized wheels
Replies: 13
Views: 3125

I studied rolling wheels on my walk back from school and I'm now also completely certain that the synchronizing effect is caused by the cleanliness and uniformity of the wheels that produce said effect. EDIT for comprehension: Uniformity meaning one wheel doesn't have one broken plastic hub cap spok...
by aguacate
Tue Aug 14, 2007 9:16 pm UTC
Forum: Science
Topic: Synchronized wheels
Replies: 13
Views: 3125

I don't think it's confirmation bias so much as it might be an optical illusion. I'm not recognizing any patterns here, just every once in a while the two wheels rolling to a stop catch my eye. This would be almost a classic example of confirmation bias; the only time you notice an experiment is wh...
by aguacate
Tue Aug 14, 2007 8:54 pm UTC
Forum: Science
Topic: Synchronized wheels
Replies: 13
Views: 3125

I don't think it's confirmation bias so much as it might be an optical illusion. I'm not recognizing any patterns here, just every once in a while the two wheels rolling to a stop catch my eye. I do not mean that assuming the wheels had a logo, the logo is pointing in the same direction for both whe...
by aguacate
Mon Aug 13, 2007 11:01 pm UTC
Forum: Science
Topic: Synchronized wheels
Replies: 13
Views: 3125

Synchronized wheels

Every once in a while I'll notice on certain cars that as they roll to a stop their front and rear wheels appear perfectly synchronized. This is only with certain cars though (usually the nicer ones). It has nothing to do with whether the wheels are on the same phase or not. What is the explanation ...
by aguacate
Sat Aug 11, 2007 11:57 pm UTC
Forum: Mathematics
Topic: Natural complements - C and S
Replies: 29
Views: 4174

C'mon, slice and cut. Ummmm. Complimentary and set.
by aguacate
Thu Aug 09, 2007 4:58 pm UTC
Forum: Mathematics
Topic: Capital letter pi
Replies: 25
Views: 6524

The second one looks like an application of the first formula with n = 3.
by aguacate
Wed Aug 08, 2007 4:29 pm UTC
Forum: Mathematics
Topic: Proving something by proving its unprovable.
Replies: 25
Views: 5901

Nosforit wrote:Hm... Wonder if you'd discover something interesting if you enumerated all possible axioms... :)


Again, this is what we're talking about. Emphasis added.
by aguacate
Wed Aug 08, 2007 2:25 am UTC
Forum: Mathematics
Topic: Percentage of reals rational
Replies: 74
Views: 12705

Dakk wrote:I haven't read the whole thread, but here's my semi-formal proof for the ratio of rationals...


Very nice, this is one of the clearest explanations I've read so far. Now that I read it, I realize my thought process was very inconsistent, but then again, of course it was.
by aguacate
Wed Aug 08, 2007 1:32 am UTC
Forum: Mathematics
Topic: Proving something by proving its unprovable.
Replies: 25
Views: 5901

not to derail the course of the thread (yeah right) but what is the precise definition of enumerate in the mathematical sense? The definitions I am familiar with are 1. Ascertain the number of something 2. To name the elements of a list one by one In which case the answer to the original axiom quest...
by aguacate
Tue Aug 07, 2007 6:57 pm UTC
Forum: Mathematics
Topic: Proving something by proving its unprovable.
Replies: 25
Views: 5901

What do you mean? You wouldn't stop. There are infinitely many possible axioms after all... This is my point... You can't do it. Well, the main target of Godel was Peano Arithmetic, which is the theory of the natural numbers with addition and multiplication, the successor function, and the usual or...
by aguacate
Tue Aug 07, 2007 6:01 pm UTC
Forum: Mathematics
Topic: Proving something by proving its unprovable.
Replies: 25
Views: 5901

How would you know when to stop? Godel's incompleteness theorem affects systems with sufficient expressive power. I would also like to know what the use of sufficiently weak systems would be. As far as the irrational behaviour of humans, well, once you have a system that asserts something false, the...
by aguacate
Tue Aug 07, 2007 3:53 pm UTC
Forum: Mathematics
Topic: Proving something by proving its unprovable.
Replies: 25
Views: 5901

Nosforit wrote:Hm... Wonder if you'd discover something interesting if you enumerated all possible axioms... :)


I think you would find that you can't enumerate all possible axioms.
by aguacate
Mon Aug 06, 2007 9:58 pm UTC
Forum: Mathematics
Topic: GRE Math
Replies: 40
Views: 6017

The GMAT study book I ordered from the library finally arrived, and when I got home and opened it up I was pissed. It was only a book on the math section of the standard GRE. Which also happens to help you with the GMAT. Except that it doesn't. Anyway, if you find any study guides that are more rece...
by aguacate
Mon Aug 06, 2007 5:50 pm UTC
Forum: Mathematics
Topic: GRE Math
Replies: 40
Views: 6017

itsbob wrote:So.......trying to bring this topic back to life. Does anyone have a sample problem that actually is similar to the GRE subject test?


Try the first link in the first post in this thread.
by aguacate
Fri Aug 03, 2007 10:39 pm UTC
Forum: Mathematics
Topic: Percentage of reals rational
Replies: 74
Views: 12705

Sorry, I was referring to this: If you're asking about probability, then you need to specify a probability distribution on the reals; i.e. a procedure for picking reals according to some probabilities. There is really no single probability distribution on the reals which is "correct"; the ...
by aguacate
Fri Aug 03, 2007 5:59 pm UTC
Forum: Mathematics
Topic: using metric spaces as transformations
Replies: 3
Views: 1461

yes, do you know of any examples?
by aguacate
Fri Aug 03, 2007 5:27 pm UTC
Forum: Mathematics
Topic: Percentage of reals rational
Replies: 74
Views: 12705

Is there any way to set up an experiment to test this? I'm guessing in real life the answer would be no (I don't know of anyone that has produced "fair dice" in practice) but theoretically....
by aguacate
Fri Aug 03, 2007 5:24 pm UTC
Forum: Mathematics
Topic: using metric spaces as transformations
Replies: 3
Views: 1461

using metric spaces as transformations

I'm just learning about metric spaces and I've been thinking a bit about the possibility of using a different metrics as a transformation. Could a change to a different metric be useful in solving problems? I'm thinking along the lines of how using LaPlace transforms simplifies certain problems for ...
by aguacate
Tue Jul 31, 2007 8:13 pm UTC
Forum: Mathematics
Topic: The cocky exponential function e^x
Replies: 6
Views: 3073

dammit I said the mods here blow dammit, silence me again will you?!!
by aguacate
Fri Jul 27, 2007 5:49 pm UTC
Forum: Mathematics
Topic: multiplying integrals
Replies: 2
Views: 2801

Thats what I thought, but then you get an answer of sqrt(pi), which is presumably wrong.

EDIT: wait I think I just figured it out, in the original integrals x and y are always positive (0 to inf) so you have to stay in the first quadrant.
by aguacate
Fri Jul 27, 2007 4:51 pm UTC
Forum: Mathematics
Topic: multiplying integrals
Replies: 2
Views: 2801

multiplying integrals

Crap, studying for my intro to analysis class and I can't remember how this works. Deriving int(0 to infinity)[e^(-x^2)]dx So we call this integral I then I^2 = int(0 to infinity)[e^(-x^2)]dx*int(0 to infinity)[e^(-y^2)]dy = int(0 to infinity)[int(0 to pi/2)[e^(-r^2)rdrdθ using the transformati...
by aguacate
Thu Jul 26, 2007 6:06 pm UTC
Forum: Mathematics
Topic: Strange math thought (grid related)
Replies: 21
Views: 3546

Just use circles
by aguacate
Tue Jul 24, 2007 4:43 am UTC
Forum: Mathematics
Topic: The mathmatics of pizza:
Replies: 74
Views: 11346

I remember going to a McDonalds once and noticing that the 20 Chicken McNuggets item cost more than five times as much as the 4 Chicken McNuggets item. I went to burger king once and they wouldn't serve us because we walked up to the drive-through window. They also should've kept a padlock on the m...
by aguacate
Tue Jul 24, 2007 4:41 am UTC
Forum: Mathematics
Topic: most efficient base for prime number searching
Replies: 9
Views: 3036

But hexadecimal is translatable, and, in fact, I suspect greatly that it's easier to translate that decimal. Perhaps it's more difficult because people don't like to think of how many E's something is divisible by. Of course it's easier to translate than decimal. You would think if it helped you fi...
by aguacate
Mon Jul 23, 2007 10:22 pm UTC
Forum: Mathematics
Topic: most efficient base for prime number searching
Replies: 9
Views: 3036

2. Then you can let your computer do it. ;) Actually, this brings up a good point - any divisibility tests that would help you out in other bases would have to be translated to binary anyway for your computer to churn it out. For instance what Cosmologicon mentioned. My guess is that certain tests ...
by aguacate
Mon Jul 23, 2007 3:56 pm UTC
Forum: Mathematics
Topic: Larger than Clarkkkson?
Replies: 11
Views: 2807

Yes it would
by aguacate
Mon Jul 23, 2007 4:49 am UTC
Forum: Mathematics
Topic: most efficient base for prime number searching
Replies: 9
Views: 3036

most efficient base for prime number searching

I just read that hexadecimal is less efficient than decimal, which led to the following question: Which is the most efficient base for searching for prime numbers?
by aguacate
Sat Jul 21, 2007 6:53 pm UTC
Forum: Mathematics
Topic: Probability
Replies: 9
Views: 2438

For problem b, it is simpler to think of the couples as individuals, and the 8 seats as 4 seats since the couples are attached and cannot be seperated nor rearranged (rearranged as in H to the right of W). Then you have (8/2)! = 4! Not sure if this is what your asking?
by aguacate
Sat Jul 21, 2007 6:48 pm UTC
Forum: Mathematics
Topic: GRE Math
Replies: 40
Views: 6017

I guess I had just forgotten the definition of a vector space. I was thinking along the lines of region where you can have two regions of the same dimension but never intersect. OK, so what about in a 3 dimensional vector space, lets say you have 2 subspaces of 2 dimensions, V1 and V2. What if V1 an...
by aguacate
Sat Jul 21, 2007 1:06 am UTC
Forum: Mathematics
Topic: GRE Math
Replies: 40
Views: 6017

haha, yeah, I asked that then I realized it was a dumb question. My mind was fried from doing all the questions. I had a fun time doing them too though. Gotta catch up on my linear algebra, well not really, but the 6 dimensional vector subspaces in a 10 dimensional vector space threw me off. When it...
by aguacate
Fri Jul 20, 2007 11:47 pm UTC
Forum: Mathematics
Topic: GRE Math
Replies: 40
Views: 6017

GRE Math

I'm getting ready to take the GRE Math test. Any advice on how to prepare? Looks fairly straightforward from the practice test but it looks like she can be a bitch in a few places.

http://www.ets.org/Media/Tests/GRE/pdf/Math.pdf
by aguacate
Thu Jul 19, 2007 5:21 pm UTC
Forum: Mathematics
Topic: Really huge numbers
Replies: 30
Views: 4486

I understand that BB is uncomputable because it grows too fast. Doesn't this automatically mean it gets bigger than any computable function? Although I see your point that we don't really know when it overtakes other functions.
by aguacate
Thu Jul 19, 2007 4:14 pm UTC
Forum: Mathematics
Topic: Really huge numbers
Replies: 30
Views: 4486

I still think BB gets bigger. And the fact that it's not computable makes things difficult, sure, but that doesn't mean that it's not well defined nor that you can't find the values for specific inputs. In fact we've got 0, 1, 4, 6, 13 from OEIS. After that it starts getting big.
by aguacate
Tue Jul 17, 2007 6:39 pm UTC
Forum: Mathematics
Topic: Favourite Erroneous "Proofs"
Replies: 194
Views: 43831

I saw a geometric proof once that every angle was a right angle, which I enjoyed very much. I think it's pretty well known; a version of it may be found here . Can I get a little help here? It seems to me that the error comes in with doing angle subtraction on dissimilar parts of congruent triangle...
by aguacate
Tue Jul 17, 2007 1:55 am UTC
Forum: Science
Topic: Science in the bible
Replies: 160
Views: 17058

Ok anything in the bible that is against our current sciences is BULL Anything in the bible that isn't against our current sciences is as true as any other thing that isn't against our current sciences that we could claim about thousands of years ago. Point: Bible is Bull. True for other religious ...
by aguacate
Mon Jul 16, 2007 11:50 pm UTC
Forum: Mathematics
Topic: Really huge numbers
Replies: 30
Views: 4486

Skewes number doesn't come close. You can't even write down the tower power that graham's number creates, it's so big.
by aguacate
Mon Jul 16, 2007 10:13 pm UTC
Forum: Mathematics
Topic: Really huge numbers
Replies: 30
Views: 4486

Yes. F(X) = C(X) + 1.

Haha, ok, but actually, if I were in a huge number contest I would write

H(X) = BB(A(x^G, x^G))

Where G is grahams number of course, A(n, m) is ackermans function and BB(x) is the busy beaver function.

H(0) = 1
H(1) = 6
H(2) = ?????
by aguacate
Mon Jul 16, 2007 3:46 pm UTC
Forum: Mathematics
Topic: Can't find a proof
Replies: 7
Views: 1865

I think you made a mistake on 1983749830893.
by aguacate
Thu Jul 12, 2007 7:21 pm UTC
Forum: Mathematics
Topic: Percentage of reals rational
Replies: 74
Views: 12705

For simplicity, let's just work with [0,1]. The rationals in this interval are countable, so assume that the complete list of rationals is q_1, q_2, q_3, etc. Now the first step of the random generator method is to flip an infinite sequence of coins. If the first coin comes up tails, then the rando...

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