Search found 1752 matches

by Token
Wed Mar 03, 2010 4:55 pm UTC
Forum: Gaming
Topic: EVE Online
Replies: 4828
Views: 647364

Re: EVE Online

And yes, the most likely cause is misunderstanding market mechanics, probably from people coming from other MMOs. You can't buy from a specific sell order, even if you right click on the order and click buy. The sale is always filled by the lowest-price order (in the same station) that can match th...
by Token
Wed Mar 03, 2010 4:39 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66290

Re: Wrong on the Internet: John Gabriel

What that proof shows is that if you have a surjection from the natural numbers to the reals that you can prove is a surjection, then you have proven mathematics inconsistent, because you also have a proof that it isn't a surjection. That's an incredibly tortured way of saying "the proof shows...
by Token
Wed Mar 03, 2010 1:34 am UTC
Forum: Mathematics
Topic: Quick question on basic topology
Replies: 18
Views: 2307

Re: Quick question on basic topology

Suffusion of Yellow wrote:The closure of the set of rationals is the set of reals

Yes: Q is dense in R.
Suffusion of Yellow wrote:The irrationals are boundary points of the set of rationals

Yes - in fact, the boundary of Q is the whole of R.
by Token
Wed Mar 03, 2010 12:19 am UTC
Forum: Gaming
Topic: EVE Online
Replies: 4828
Views: 647364

Re: EVE Online

OK - here's the situation. As luck / compulsive undercutting would have it, a few minutes ago I happened to have the best sell order for Warrior IIs at a particular trade hub. Now, also at this hub, for reasons that are unclear to me but probably have something to do with misunderstanding how the ma...
by Token
Tue Mar 02, 2010 9:17 pm UTC
Forum: Mathematics
Topic: Taylor Expansion of f:R^n->R
Replies: 5
Views: 760

Re: Taylor Expansion of f:R^n->R

The Taylor series for a function f: R^n \to R about the point a \in R^n is: \sum_{k_1,\ldots,k_n \geq 0} \left[\cfrac{(x_1 - a_1)^{k_1} \ldots (x_n - a_n)^{k_n}}{k_1! \ldots k_n!}\cfrac{\partial^{k_1+\ldots + k_n}}{\partial x_1^{k_1} \ldots \partial x_n^{k_n}}f(a_1,\ldots,a_n)...
by Token
Mon Mar 01, 2010 5:12 pm UTC
Forum: Mathematics
Topic: slightly excessive numbers
Replies: 6
Views: 1377

Re: slightly excessive numbers

kernelpanic wrote:
Anubis wrote:Yeah, if you counted the number itself, every number would work.

Except 1. And 0.

And every other non-prime number.
by Token
Mon Mar 01, 2010 1:13 pm UTC
Forum: Mathematics
Topic: Determinants in the Projective Special Linear Group?
Replies: 6
Views: 1177

Re: Determinants in the Projective Special Linear Group?

Yes, all the matrices associated with a certain transformation have determinants that are the same up to multiplication by a square, but that's not what's being asked... This is actually exactly what you want to know to answer the question. Let me try and explain what's going on a bit more rigorous...
by Token
Sun Feb 28, 2010 8:45 pm UTC
Forum: Mathematics
Topic: Determinants in the Projective Special Linear Group?
Replies: 6
Views: 1177

Re: Determinants in the Projective Special Linear Group?

The problem here is that the question is slightly badly worded - PSL(2,F) is not a group of matrices (it is the quotient of such a group), and Möbius transformations don't have determinants. What we're actually doing is viewing PSL(2,F) as a group of Möbius transformations, and trying to show that a...
by Token
Sun Feb 28, 2010 5:04 pm UTC
Forum: Mathematics
Topic: Determinants in the Projective Special Linear Group?
Replies: 6
Views: 1177

Re: Determinants in the Projective Special Linear Group?

Consider the matrices [imath]\begin{pmatrix}a & b \\ c & d\end{pmatrix}[/imath] and [imath]\begin{pmatrix}ka & kb \\ kc & kd\end{pmatrix}[/imath]. How are their associated transformations related? What about their determinants?
by Token
Thu Feb 25, 2010 6:24 pm UTC
Forum: Gaming
Topic: EVE Online
Replies: 4828
Views: 647364

Re: EVE Online

Huh. Apparently if I forget to buy a PLEX for my account and it expires, the GMs are willing to reactivate it for a day so I can get one. I approve of this policy.
by Token
Thu Feb 25, 2010 1:38 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66290

Re: Wrong on the Internet: John Gabriel

Azrael wrote:PROTIP: The axes aren't actually there.

*headdesk*
by Token
Wed Feb 24, 2010 9:42 pm UTC
Forum: Mathematics
Topic: Differentiating rational functions with no constants.
Replies: 2
Views: 426

Re: Differentiating rational functions with no constants.

The derivative of ax+b is not a+b.
by Token
Wed Feb 24, 2010 6:50 pm UTC
Forum: Mathematics
Topic: How does one solve the Navier Stokes Equations?
Replies: 23
Views: 3360

Re: How does one solve the Navier Stokes Equations?

jestingrabbit wrote:Weird that nothing has come of that. Not a retraction, nor an explicit counterexample. Weird.

http://web.archive.org/web/200706230203 ... etz/RH.pdf claims the disproof was flawed.
by Token
Tue Feb 23, 2010 9:40 pm UTC
Forum: Mathematics
Topic: Division by Zero (Please, no new threads about this)
Replies: 367
Views: 84460

Re: Division by Zero (Please, no new threads about this)

hawkmp4 wrote:You don't have to define division by zero, no. But if 0/0 is unequivocally undefined then calculus means nothing. From the definition of a derivative on.

Umm... no. No, not at all. Calculus doesn't require division by zero anywhere.
by Token
Tue Feb 23, 2010 9:08 pm UTC
Forum: Mathematics
Topic: How does one solve the Navier Stokes Equations?
Replies: 23
Views: 3360

Re: How does one solve the Navier Stokes Equations?

Actually, Navier-Stokes and P = NP are the only two that are automatically prize candidates either way. The others get discretionary prizes for counterexamples (up to the full million), depending on how well the original problem survives the counterexample after any necessary reformulation.
by Token
Mon Feb 22, 2010 1:57 pm UTC
Forum: Mathematics
Topic: "Lowest Unique" auction / lottery
Replies: 18
Views: 2101

Re: "Lowest Unique" auction / lottery

I suppose people are strictly forbidden to communicate? Otherwise someone can just be the first to choose "1", and tell everyone that she did so. After that, no one else can win by picking 1, and no one can win by picking another number. Well, if at least one other person picks 1, then ot...
by Token
Mon Feb 22, 2010 12:00 am UTC
Forum: Mathematics
Topic: Morphisms of varieties
Replies: 8
Views: 1375

Re: Morphisms of varieties

Indeed - in fact, I believe it's a well-known result that given any two fields of mathematical study, it is possible to pair theorems from the two fields in such a way that each pair consists of two special cases of the same general theorem of category theory.
by Token
Thu Feb 18, 2010 7:52 am UTC
Forum: Mathematics
Topic: Matrix Algebra question about identity matricies and scalars
Replies: 12
Views: 1366

Re: Matrix Algebra question about identity matricies and scalars

Yes, but the relevant part of the [imath]f: \lambda \mapsto \lambda I[/imath] isomorphism is that [imath]\lambda \times_S A = f(\lambda) \times_M A[/imath] for any scalar [imath]\lambda[/imath] and matrix [imath]A[/imath].
by Token
Wed Feb 17, 2010 11:25 pm UTC
Forum: Mathematics
Topic: Matrix Algebra question about identity matricies and scalars
Replies: 12
Views: 1366

Re: Matrix Algebra question about identity matricies and scalars

So what you mean is an isomorphism between the field of scalars and the field of matrices of the form λI.
by Token
Mon Feb 15, 2010 9:05 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0702: "Snow Tracking"
Replies: 135
Views: 38631

Re: “Snow Tracking” discussion

Oh, because the electronic throttle got stuck... I see. It's still not very good. Why did Calvin stop in several different places to use the duplicator? And why does Long Cat have such a long stride? It has a long body, not long feet... Like a limousine. Longcat has a long stride because hes long o...
by Token
Thu Feb 11, 2010 11:26 pm UTC
Forum: Mathematics
Topic: Largest number on Twitter
Replies: 70
Views: 10521

Re: Largest number on Twitter

BlackSails wrote:The smallest number that cannot be defined in a tweet is:
"the largest number that can be defined in a tweet +1"

Why should the smallest undefinable number be larger than the largest definable number?
by Token
Thu Feb 11, 2010 11:01 pm UTC
Forum: Serious Business
Topic: Deconversion to atheism; an interesting journey
Replies: 14
Views: 3278

Re: Deconversion to atheism; an interesting journey

What evidence do you require to know that something is morally OK versus morally wrong? That depends on what you mean by "morally OK" / "morally wrong". When someone says they believe something is morally wrong, that's almost certainly hinging on an unspoken and probably ill-def...
by Token
Thu Feb 11, 2010 7:47 pm UTC
Forum: Gaming
Topic: EVE Online
Replies: 4828
Views: 647364

Re: EVE Online

Xaddak wrote:Palindromes.

Guess again.

EDIT: Bah, stop explicitly pointing out his error. That takes all the fun out of it...
by Token
Thu Feb 11, 2010 7:41 pm UTC
Forum: Gaming
Topic: EVE Online
Replies: 4828
Views: 647364

Re: EVE Online

Xaddak wrote:Deker is, and Decer is, but Decker is not.

Umm... what?
by Token
Thu Feb 11, 2010 6:55 pm UTC
Forum: Serious Business
Topic: Deconversion to atheism; an interesting journey
Replies: 14
Views: 3278

Re: Deconversion to atheism; an interesting journey

Is it more prudent to wonder if it is more prudent to wonder if a belief is warranted in the first place? What is the need for or evidence for the belief that if a belief is without need or evidence you should default to not having it? I get the feeling that you're not looking for a real response, ...
by Token
Wed Feb 10, 2010 6:22 pm UTC
Forum: Mathematics
Topic: Largest number on Twitter
Replies: 70
Views: 10521

Re: Largest number on Twitter

(Or another way of looking at it, the arithmetic symbols are going to no better than just adding more symbols like A, B, C to increase the radix of the representation.) Actually, from the point of view of maximising the smallest non-representable number, the arithmetic symbols are necessarily going...
by Token
Tue Feb 09, 2010 10:14 pm UTC
Forum: Mathematics
Topic: Largest number on Twitter
Replies: 70
Views: 10521

Re: Largest number on Twitter

You definitely need the parentheses. "^" isn't associative, so "9^9^9^9" is ambiguous. There's usually a convention that exponentiation is right-associative, so "x^y^z" is typically taken to mean "x^(y^z)" (and as such is unambiguous). This is obviously sensi...
by Token
Mon Feb 08, 2010 1:51 pm UTC
Forum: Serious Business
Topic: Old games and ethics.
Replies: 43
Views: 6140

Re: Old games and ethics.

There is a large difference between not being given the offer to trade copiable intellectual property because the seller has deemed it to no longer be commercially viable to continue making such an offer public, and, say, active refusal to trade a uniquely valuable physical item. You can't just crea...
by Token
Mon Feb 08, 2010 1:00 pm UTC
Forum: Serious Business
Topic: Old games and ethics.
Replies: 43
Views: 6140

Re: Old games and ethics.

And the rule for when the other side doesn't offer or accept: you can't just take what you want anyway . This merits challenging. Why not? (I'm going to interpret "can't" to mean "shouldn't", rather than "aren't legally permitted to", as I don't think anyone's debating...
by Token
Fri Feb 05, 2010 10:14 pm UTC
Forum: Forum Games
Topic: Create a Card: MTG
Replies: 3761
Views: 406104

Re: Create a Card: MTG

mosc wrote:You can't twiddle it, you have no cards to twiddle with.

You'll have cards until its enters-the-battlefield ability resolves, which is plenty of time to untap it.
by Token
Thu Feb 04, 2010 8:50 am UTC
Forum: Mathematics
Topic: Infinity
Replies: 31
Views: 4099

Re: Infinity

btw, from the fact that ln(a b ) = b ln(a), you can pretty quickly come to a precise expression for ln(googol^googol), which is C*10^102. Not sure what happened to alpha on that one. I'm guessing the OP just misremembered the number after the decimal point. Wolfram Alpha gives the correct answer wh...
by Token
Tue Feb 02, 2010 5:46 am UTC
Forum: Mathematics
Topic: Base 10 or Base A?
Replies: 16
Views: 1790

Re: Base 10 or Base A?

Same difference. "Inductive definition" and "recursive definition" are synonyms. Sure. Would you say "induction" and "recursion" are also synonymous? You're right, I lied. I wanted to make the point that you can't actually tell anything at all about that set ...
by Token
Mon Feb 01, 2010 7:16 pm UTC
Forum: Mathematics
Topic: Base 10 or Base A?
Replies: 16
Views: 1790

Re: Base 10 or Base A?

If I'm aiming to be especially unambiguous, I write "nine plus one." Induction wins. Well, if I'm going to name the elements of a set, I'd prefer to do it before defining extraneous binary operators on that set, if possible. Oh, and I'm moderately sure you mean recursion, not induction. :...
by Token
Mon Feb 01, 2010 3:42 pm UTC
Forum: Mathematics
Topic: Base 10 or Base A?
Replies: 16
Views: 1790

Re: Base 10 or Base A?

For instance I read "0x4B" as "forty-bee", or "0xff" as "effty-eff" For larger numbers like memory addresses I switch back to spelling digit by digit. We should make a poll! It's the obvious way to do it, but you run into difficulty when, say, trying to disti...
by Token
Mon Feb 01, 2010 10:23 am UTC
Forum: Mathematics
Topic: HW question regarding supremums
Replies: 13
Views: 1026

Re: HW question regarding supremums

Well, certainly if you're writing a textbook or using it as a lemma, you should cover all the cases. But if you're setting homework, I'm not sure if it isn't worth just leaving it out. You might end up confusing more students than you enlighten. But then, I'm not a teacher.
by Token
Mon Feb 01, 2010 10:15 am UTC
Forum: Mathematics
Topic: HW question regarding supremums
Replies: 13
Views: 1026

Re: HW question regarding supremums

EDIT: Never mind. You clearly ninja-edited me.
by Token
Mon Feb 01, 2010 10:10 am UTC
Forum: Mathematics
Topic: Base 10 or Base A?
Replies: 16
Views: 1790

Re: Base 10 or Base A?

"Ten" does not mean "10," it means "one plus one plus one plus one plus one plus one plus one plus one plus one plus one." I prefer "S(S(S(S(S(S(S(S(S(S(0))))))))))". Or maybe even "{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},{{},{{}},{{},{{}}},{{},{{}},{{},{...
by Token
Mon Feb 01, 2010 9:49 am UTC
Forum: Mathematics
Topic: HW question regarding supremums
Replies: 13
Views: 1026

Re: HW question regarding supremums

You might want to also mention the case where you have something like E_1 = {-\infty} and E_2 is the integers, or something else unbounded in the positive direction. The result isn't actually true in that case. There's probably a casual assumption that sup(E 1 + E 2 ) = sup(E 1 ) + sup(E 2 ) only h...
by Token
Sun Jan 31, 2010 11:44 am UTC
Forum: Mathematics
Topic: [solved]Commuting fucntions problem
Replies: 4
Views: 714

Re: Commuting fucntions problem

Part (b): Suppose g(x) = ax^3 + bx^2 + cx + d . If f(g(x)) = g(f(x)) , then we have that: (ax^3 + bx^2 + cx + d)^2 - 2 = a(x^2-2)^3 + b(x^2-2)^2 + c(x^2-2) + d Try expanding this out and seeing what you can say about the possibl...

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