Search found 855 matches

by Buttons
Tue Feb 10, 2009 1:17 am UTC
Forum: Mathematics
Topic: RNG in xkcd
Replies: 4
Views: 940

Re: RNG in xkcd

I believe this has already been answered.
by Buttons
Sun Feb 08, 2009 11:13 pm UTC
Forum: Logic Puzzles
Topic: D&D puzzle
Replies: 31
Views: 8906

Re: D&D puzzle

Spoiler:
Also, if the key is hanging off the edge of the table, put the keyhole of the chest around the key and turn the chest.
by Buttons
Sun Feb 08, 2009 3:36 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 457422

Re: Favorite math jokes

MartianInvader wrote:A Ramsey theorist is giving a talk, when he forgets the date of one of his references. He says, "I don't remember when this was published, but it was earlier than the year 10^ 10^ 10^ 10^ 10^ 10."

Hah! I love it.
by Buttons
Fri Feb 06, 2009 7:58 pm UTC
Forum: Mathematics
Topic: Number Game!
Replies: 64
Views: 3672

Re: Number Game!

Can you write this out without ellipsis for a specific N? That was my point exactly. But the point is, you can write out Cosmologicon's expression without ellipsis for a specific N while still only using four 4s. You can't with your example. Your argument that taking roots is "really" jus...
by Buttons
Fri Feb 06, 2009 4:12 pm UTC
Forum: Mathematics
Topic: Number Game!
Replies: 64
Views: 3672

Re: Number Game!

Can you write this out without ellipsis for a specific N?
by Buttons
Fri Feb 06, 2009 4:01 pm UTC
Forum: Mathematics
Topic: Number Game!
Replies: 64
Views: 3672

Re: Number Game!

What about exploiting order of operations and parenthesis? That's what the 5 is counting. (How many ways can you order three sets of parentheses? How many ways can you construct the binary tree for an expression involving four numbers and three binary operators? It's easy to see that this is the th...
by Buttons
Fri Feb 06, 2009 3:48 pm UTC
Forum: Mathematics
Topic: Number Game!
Replies: 64
Views: 3672

Re: Number Game!

That being said, the range of numbers which you can generate in this manner is much smaller. I haven't been able to come up with a solution for 13 yet. Yeah, it's easy to see that this is a pretty big restriction: if we're only allowed to use four 4s and our choice among n different binary operator...
by Buttons
Fri Feb 06, 2009 12:32 am UTC
Forum: Mathematics
Topic: Number Game!
Replies: 64
Views: 3672

Re: Number Game!

First of all, 117=9*sigma(9), but 4+4 isn't 9. Second, number-theoretic functions like sigma and phi make this way too easy. To wit: 117=4!*4+sigma(4)*sigma(phi(4)). I'm pretty sure, though I can't prove it, that you can get any positive even number using just one 4 and arbitrarily many sigmas and p...
by Buttons
Fri Feb 06, 2009 12:13 am UTC
Forum: Mathematics
Topic: How does the cartesian product relate to other products?
Replies: 30
Views: 2676

Re: How does the cartesian product relate to other products?

Probably not in a way you'll find very enlightening. Recall that from sets, we define the naturals, from naturals the integers, from integers the rationals, from rationals the reals. What is a matrix but an array of numbers? So the set theoretic way to define an n by n matrix is as a function from {...
by Buttons
Wed Feb 04, 2009 11:40 pm UTC
Forum: Logic Puzzles
Topic: D&D puzzle
Replies: 31
Views: 8906

Re: D&D puzzle

Go to the central chamber. Put the key in the case (being careful not to move the case), open it (does opening count as moving? I'm assuming not.), pour the vial on the message, wear the glasses, read the message, and exit through the western hallway (whose trap hasn't b...
by Buttons
Wed Feb 04, 2009 11:27 pm UTC
Forum: Mathematics
Topic: Topic 2000
Replies: 30
Views: 2483

Re: Topic 2000

I can draw a labeled tree for which it's the Prüfer code.
by Buttons
Sun Feb 01, 2009 12:56 pm UTC
Forum: Logic Puzzles
Topic: Space filling function
Replies: 9
Views: 1295

Re: Space filling function

Why are we assuming that the domain is R? f: [0,1]x[0,1] -> R2 by the natural inclusion map works fine.
by Buttons
Sat Jan 31, 2009 11:09 pm UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 2806

Re: Interesting sequences (Catalan, maybe?)

That's a closed-form expression, not a generating function.
by Buttons
Sat Jan 31, 2009 11:07 pm UTC
Forum: Mathematics
Topic: Life and math
Replies: 21
Views: 2090

Re: Life and math

Describing it as a DFA is impossible, though, because of the F part: it's on an infinite lattice, not a finite one. And while using {0,1} to represent alive or dead cells is fine, that doesn't really have anything to do with alphabets for formal languages, which are what DFAs are supposed to recogni...
by Buttons
Sat Jan 31, 2009 6:39 pm UTC
Forum: Mathematics
Topic: Life and math
Replies: 21
Views: 2090

Re: Life and math

One last resource I can think of is volume IV of Winning Ways . It probably won't contain any information that's not at Weisstein's or the Lifewiki, but it is written (at least largely) by Conway, so you might get some insights there. Something you might consider talking about is comparing the "...
by Buttons
Fri Jan 30, 2009 4:06 pm UTC
Forum: Mathematics
Topic: The continuous elevator
Replies: 15
Views: 1702

Re: The continuous elevator

To say that some dots might never get picked up but that this happens with probability 0 is not a contradiction. In fact it's true, for appropriate elevator speed.
by Buttons
Thu Jan 29, 2009 9:23 pm UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 2806

Re: Interesting sequences

Yeah, my teacher said the Catalans are too advanced. Does anyone have anything else about triangular square numbers? Seriously? I've taught fifth graders about the Catalans, but I can't imagine doing the same for triangular squares. (On a side note, since when is it the job of the teacher to tell t...
by Buttons
Wed Jan 28, 2009 9:25 pm UTC
Forum: Mathematics
Topic: License Plates
Replies: 9
Views: 632

Re: License Plates

Suppose all you care about is which characters are letters and which ones are numbers. How many ways can you pick which three of the six characters are letters?
by Buttons
Wed Jan 28, 2009 6:09 pm UTC
Forum: Mathematics
Topic: objects that we'd like to hold, but can't in this universe
Replies: 41
Views: 5664

Re: objects that we'd like to hold, but can't in this universe

Here's one. It's pretty fun to play with, too.
by Buttons
Wed Jan 28, 2009 2:58 am UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 2806

Re: Interesting sequences

Pascal's Triangle isn't really a "sequence", though. Plus, your teacher has certainly heard of it.
by Buttons
Wed Jan 28, 2009 2:17 am UTC
Forum: Mathematics
Topic: objects that we'd like to hold, but can't in this universe
Replies: 41
Views: 5664

Re: Looking for a link for these 4 and 5 dimensional graphs

gnuoym wrote:How has noone pointed to these? For all your non-orientable drinking requirements.

Has anyone else here met that guy? He hawks his goods at math meetings all the time, and let me just say: totally insane. And hilarious.
by Buttons
Wed Jan 28, 2009 2:13 am UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 2806

Re: Interesting sequences

The Catalan numbers are probably a good choice. If that's too simple, perhaps the Robbins numbers: 1, 1, 2, 7, 42, 429, 7436,.... These are known to count a few different families of objects (like alternating sign matrices or totally symmetric self-complementary plane partitions), but no bijections ...
by Buttons
Sat Jan 24, 2009 8:17 pm UTC
Forum: Mathematics
Topic: Favourite Erroneous "Proofs"
Replies: 194
Views: 40918

Re: Favourite Erroneous "Proofs"

But that part is true. Given that any k numbers are equal, it *does* follow that any k+1 numbers must be equal. Actually, I'd say this is false, since the proof fails for k=1. When resolving this paradox, I like to show that the error occurs in the inductive step. Your explanation, I've found, tend...
by Buttons
Thu Jan 22, 2009 10:07 pm UTC
Forum: Mathematics
Topic: objects that we'd like to hold, but can't in this universe
Replies: 41
Views: 5664

Re: Looking for a link for these 4 and 5 dimensional graphs

Can someone give me a link to a picture of a nonvanishing continuous vector field on a sphere?
by Buttons
Thu Jan 22, 2009 7:09 pm UTC
Forum: Mathematics
Topic: Argh... what am I not seeing? (homework problem)
Replies: 14
Views: 1609

Re: Argh... what am I not seeing? (homework problem)

Except for e-3, of course.
by Buttons
Wed Jan 21, 2009 10:37 pm UTC
Forum: Mathematics
Topic: MATH PUZZLE!
Replies: 25
Views: 2052

Re: MATH PUZZLE!

I think it's a (cup of ((tea and cheese) sandwich)).
by Buttons
Mon Jan 19, 2009 7:39 pm UTC
Forum: Mathematics
Topic: MATH PUZZLE!
Replies: 25
Views: 2052

Re: MATH PUZZLE!

Plus, doesn't the Greenhouse accept some sort of meal equivalency? At the very least, I've seen people swipe student cards there, which might not count as "dollars paid" if it's some sort of dining hall-only currency.
by Buttons
Fri Jan 16, 2009 4:59 pm UTC
Forum: Mathematics
Topic: How many triangles?
Replies: 16
Views: 7273

Re: How many triangles?

I meant literally any diagram made of straight lines. I know there might not be a straightforward answer, but if there is one I thought here would be the place to try and find it. Sure. Take the total number of triples of vertices ( n \choose 3 , where n is the number of vertices), subtract the num...
by Buttons
Fri Jan 16, 2009 4:24 pm UTC
Forum: Mathematics
Topic: For every and equivalents
Replies: 13
Views: 1234

Re: For every and equivalents

epigram wrote:Not to belabor the subject, but am I correct in my assumption that there is a distinct difference between the statements 'continuous at a' and 'continuous at a point a.'

In the right context, I see no difference between those statements. What do you think the difference is?
by Buttons
Wed Jan 14, 2009 1:01 pm UTC
Forum: Mathematics
Topic: Beginner Stuff
Replies: 23
Views: 2138

Re: Beginner Stuff

I'm not sure what you mean. The union of A and B is \{ x | x \in A \text{ or } x \in B \} . Right, but in some situations it's nice to be able to say that the union of \lbrace a_1,a_2,\dots,a_n\rbrace and \lbrace b_1,b_2,\dots,b_m\rbrace is \lbrace a_1,a_2,\dots,a_n,b_1,b_2,\dots,b_m\rbrace without...
by Buttons
Tue Jan 13, 2009 11:49 pm UTC
Forum: Mathematics
Topic: Periodic function mapping to {0,1}
Replies: 17
Views: 1417

Re: Periodic function mapping to {0,1}

Are we to assume, from your notion of "pulse", that you want each element of f-1(1) to be an isolated point?
by Buttons
Tue Jan 13, 2009 11:46 pm UTC
Forum: Mathematics
Topic: Beginner Stuff
Replies: 23
Views: 2138

Re: Beginner Stuff

Sets don't have repeated elements, or a set with repetitions is equivalent to one with repetitions removed? I go with the latter, which makes certain unions easier to write. Say I'm going to flip a coin and roll a die 100 times and collect the data as a set of ordered pairs. Wouldn't that set neces...
by Buttons
Tue Jan 13, 2009 7:03 pm UTC
Forum: Mathematics
Topic: For every and equivalents
Replies: 13
Views: 1234

Re: For every and equivalents

Right. When you see "for all", imagine that a demon is giving you the number.

Demons, you may recall, have pointy chins, triangular faces, and two horns. They look sort of like this:[math]\forall[/math]
by Buttons
Thu Jan 08, 2009 12:42 pm UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 5605

Re: Prove that two curves in a square intersect

Okay, but the point is that this proof won't work: you won't be able to find such a homeomorphism, because in general it doesn't exist.
by Buttons
Thu Jan 08, 2009 11:59 am UTC
Forum: Logic Puzzles
Topic: Choice by coin flipping
Replies: 28
Views: 4903

Re: 3-sided coin *emulation*

That's what I thought at first, jaap, but that one takes 3 flips (1 + 1 + 1/2 + 1/4 + 1/8 + ...) on average to pick between A, B and C, whereas SS's only takes 8/3. I was surprised by this result, for what it's worth. That method seemed so natural that I assumed it would be best. I think my proof of...
by Buttons
Thu Jan 08, 2009 11:51 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 5605

Re: Prove that two curves in a square intersect

If you're saying you want a homeomorphism between Im(c) ∪ Im(d) and the union of two lines with the same endpoints, you won't find it, since the former might actually have more (distinct) intersections than the latter.
by Buttons
Thu Jan 08, 2009 3:14 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 5605

Re: Prove that two curves in a square intersect

If they use it, they use a particularly simplified version. For instance, my first proof only requires that it hold for lattice paths.
by Buttons
Thu Jan 08, 2009 2:34 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 5605

Re: Prove that two curves in a square intersect

Then you haven't read closely enough, I guess? There have been a few proofs in this thread so far, all of which are much simpler than any proof of JCT.
by Buttons
Wed Jan 07, 2009 11:11 pm UTC
Forum: Mathematics
Topic: Boy or Girl Paradox
Replies: 126
Views: 12006

Re: Boy or Girl Paradox

Again, would someone like to address my point? If the statement can refer to either child, then GG and GG are two separate events, for precisely the same reason BG and GB are considered seperate events. It's been addressed quite a few times, but sure: the statement doesn't refer to a child. It refe...
by Buttons
Wed Jan 07, 2009 10:47 pm UTC
Forum: Mathematics
Topic: Boy or Girl Paradox
Replies: 126
Views: 12006

Re: Boy or Girl Paradox

You really have no intention of responding to the posts in which you're proven wrong, do you?

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