## Search found 855 matches

- Tue Feb 10, 2009 1:17 am UTC
- Forum: Mathematics
- Topic: RNG in xkcd
- Replies:
**4** - Views:
**957**

### Re: RNG in xkcd

I believe this has already been answered.

- Sun Feb 08, 2009 11:13 pm UTC
- Forum: Logic Puzzles
- Topic: D&D puzzle
- Replies:
**31** - Views:
**9355**

### Re: D&D puzzle

**Spoiler:**

- Sun Feb 08, 2009 3:36 am UTC
- Forum: Mathematics
- Topic: Favorite math jokes
- Replies:
**1452** - Views:
**468490**

### 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.

- Fri Feb 06, 2009 7:58 pm UTC
- Forum: Mathematics
- Topic: Number Game!
- Replies:
**64** - Views:
**3928**

### 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...

- Fri Feb 06, 2009 4:12 pm UTC
- Forum: Mathematics
- Topic: Number Game!
- Replies:
**64** - Views:
**3928**

### Re: Number Game!

Can you write this out without ellipsis for a specific N?

- Fri Feb 06, 2009 4:01 pm UTC
- Forum: Mathematics
- Topic: Number Game!
- Replies:
**64** - Views:
**3928**

### 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...

- Fri Feb 06, 2009 3:48 pm UTC
- Forum: Mathematics
- Topic: Number Game!
- Replies:
**64** - Views:
**3928**

### 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...

- Fri Feb 06, 2009 12:32 am UTC
- Forum: Mathematics
- Topic: Number Game!
- Replies:
**64** - Views:
**3928**

### 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...

- Fri Feb 06, 2009 12:13 am UTC
- Forum: Mathematics
- Topic: How does the cartesian product relate to other products?
- Replies:
**30** - Views:
**2845**

### 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 {...

- Wed Feb 04, 2009 11:40 pm UTC
- Forum: Logic Puzzles
- Topic: D&D puzzle
- Replies:
**31** - Views:
**9355**

### 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...

- Wed Feb 04, 2009 11:27 pm UTC
- Forum: Mathematics
- Topic: Topic 2000
- Replies:
**30** - Views:
**2686**

### Re: Topic 2000

I can draw a labeled tree for which it's the Prüfer code.

- Sun Feb 01, 2009 12:56 pm UTC
- Forum: Logic Puzzles
- Topic: Space filling function
- Replies:
**9** - Views:
**1330**

### Re: Space filling function

Why are we assuming that the domain is R? f: [0,1]x[0,1] -> R

^{2}by the natural inclusion map works fine.- Sat Jan 31, 2009 11:09 pm UTC
- Forum: Mathematics
- Topic: Interesting sequences (Catalan, maybe?)
- Replies:
**42** - Views:
**3073**

### Re: Interesting sequences (Catalan, maybe?)

That's a closed-form expression, not a generating function.

- Sat Jan 31, 2009 11:07 pm UTC
- Forum: Mathematics
- Topic: Life and math
- Replies:
**21** - Views:
**2191**

### 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...

- Sat Jan 31, 2009 6:39 pm UTC
- Forum: Mathematics
- Topic: Life and math
- Replies:
**21** - Views:
**2191**

### 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 "...

- Fri Jan 30, 2009 4:06 pm UTC
- Forum: Mathematics
- Topic: The continuous elevator
- Replies:
**15** - Views:
**1827**

### 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.

- Thu Jan 29, 2009 9:23 pm UTC
- Forum: Mathematics
- Topic: Interesting sequences (Catalan, maybe?)
- Replies:
**42** - Views:
**3073**

### 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...

- Wed Jan 28, 2009 9:25 pm UTC
- Forum: Mathematics
- Topic: License Plates
- Replies:
**9** - Views:
**662**

### 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?

- 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:
**5898**

### 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.

- Wed Jan 28, 2009 2:58 am UTC
- Forum: Mathematics
- Topic: Interesting sequences (Catalan, maybe?)
- Replies:
**42** - Views:
**3073**

### Re: Interesting sequences

Pascal's Triangle isn't really a "sequence", though. Plus, your teacher has certainly heard of it.

- 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:
**5898**

### 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.

- Wed Jan 28, 2009 2:13 am UTC
- Forum: Mathematics
- Topic: Interesting sequences (Catalan, maybe?)
- Replies:
**42** - Views:
**3073**

### 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 ...

- Sat Jan 24, 2009 8:17 pm UTC
- Forum: Mathematics
- Topic: Favourite Erroneous "Proofs"
- Replies:
**194** - Views:
**41912**

### 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...

- 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:
**5898**

### 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?

- Thu Jan 22, 2009 7:09 pm UTC
- Forum: Mathematics
- Topic: Argh... what am I not seeing? (homework problem)
- Replies:
**14** - Views:
**1857**

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

Except for e

^{-3}, of course.- Wed Jan 21, 2009 10:37 pm UTC
- Forum: Mathematics
- Topic: MATH PUZZLE!
- Replies:
**25** - Views:
**2177**

### Re: MATH PUZZLE!

I think it's a (cup of ((tea and cheese) sandwich)).

- Mon Jan 19, 2009 7:39 pm UTC
- Forum: Mathematics
- Topic: MATH PUZZLE!
- Replies:
**25** - Views:
**2177**

### 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.

- Fri Jan 16, 2009 4:59 pm UTC
- Forum: Mathematics
- Topic: How many triangles?
- Replies:
**16** - Views:
**7336**

### 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...

- Fri Jan 16, 2009 4:24 pm UTC
- Forum: Mathematics
- Topic: For every and equivalents
- Replies:
**13** - Views:
**1304**

### 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?

- Wed Jan 14, 2009 1:01 pm UTC
- Forum: Mathematics
- Topic: Beginner Stuff
- Replies:
**23** - Views:
**2256**

### 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...

- Tue Jan 13, 2009 11:49 pm UTC
- Forum: Mathematics
- Topic: Periodic function mapping to {0,1}
- Replies:
**17** - Views:
**1503**

### 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?- Tue Jan 13, 2009 11:46 pm UTC
- Forum: Mathematics
- Topic: Beginner Stuff
- Replies:
**23** - Views:
**2256**

### 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...

- Tue Jan 13, 2009 7:03 pm UTC
- Forum: Mathematics
- Topic: For every and equivalents
- Replies:
**13** - Views:
**1304**

### 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]

Demons, you may recall, have pointy chins, triangular faces, and two horns. They look sort of like this:[math]\forall[/math]

- Thu Jan 08, 2009 12:42 pm UTC
- Forum: Mathematics
- Topic: Prove that two curves in a square intersect
- Replies:
**76** - Views:
**5993**

### 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.

- Thu Jan 08, 2009 11:59 am UTC
- Forum: Logic Puzzles
- Topic: Choice by coin flipping
- Replies:
**28** - Views:
**5028**

### 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...

- Thu Jan 08, 2009 11:51 am UTC
- Forum: Mathematics
- Topic: Prove that two curves in a square intersect
- Replies:
**76** - Views:
**5993**

### 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.

- Thu Jan 08, 2009 3:14 am UTC
- Forum: Mathematics
- Topic: Prove that two curves in a square intersect
- Replies:
**76** - Views:
**5993**

### 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.

- Thu Jan 08, 2009 2:34 am UTC
- Forum: Mathematics
- Topic: Prove that two curves in a square intersect
- Replies:
**76** - Views:
**5993**

### 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.

- Wed Jan 07, 2009 11:11 pm UTC
- Forum: Mathematics
- Topic: Boy or Girl Paradox
- Replies:
**126** - Views:
**12519**

### 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...

- Wed Jan 07, 2009 10:47 pm UTC
- Forum: Mathematics
- Topic: Boy or Girl Paradox
- Replies:
**126** - Views:
**12519**

### Re: Boy or Girl Paradox

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