Search found 825 matches

by Torn Apart By Dingos
Thu Mar 04, 2010 10:21 pm UTC
Forum: Mathematics
Topic: LaTeX equation numbering
Replies: 6
Views: 6470

Re: LaTeX equation numbering

As others have said, don't use \begin{eqnarray}. It doesn't handle spacing properly. Use \begin{align} or \begin{gather} (both have starred versions, if you don't want numbering). In both you can type several lines of equations. Inside either of these, you can use \begin{split} to write multiple equ...
by Torn Apart By Dingos
Thu Mar 04, 2010 9:59 pm UTC
Forum: Mathematics
Topic: Chain email
Replies: 28
Views: 3631

Re: Chain email

I object to it in this case precisely because it's not an equivalence relation. So the object is to the use of "=" as an assignment operator? It's used that way in most programming languages, and I think statements like "Solve for f(x) given x=5" are common enough to justify usi...
by Torn Apart By Dingos
Wed Mar 03, 2010 7:45 pm UTC
Forum: Mathematics
Topic: Chain email
Replies: 28
Views: 3631

Re: Chain email

which really grinded my gears. Don't change the meaning of the equality sign! Why not? Equivalence relations are all over the place, and it clutters things up to use a different symbol. Do you object to the use of "=" for natural, rational, real and complex numbers even though the relatio...
by Torn Apart By Dingos
Tue Mar 02, 2010 10:12 am UTC
Forum: Mathematics
Topic: Chain email
Replies: 28
Views: 3631

Re: Chain email

Another vote for that the notation of this puzzle is stupid. In this case it might be okay, since it's just replacing the + operator (but I'd rather it be another operator), but I've seen puzzles in the form of 1 = 7 2 = 6 3 = 10 4 = 1 ... which really grinded my gears. Don't change the meaning of t...
by Torn Apart By Dingos
Fri Jan 01, 2010 4:41 pm UTC
Forum: Mathematics
Topic: How come all numbers aren't undefined?
Replies: 31
Views: 3326

Re: How come all numbers aren't undefined?

It is rather simple. You cannot reorder or re-associate a conditionally convergent infinite sum. I was wondering about that. Why can't you? Really, why should it lead to a contradiction. It's easy to say "don't do this, it won't work" but I'm wondering why it won't work. Why does the norm...
by Torn Apart By Dingos
Fri Nov 20, 2009 8:28 pm UTC
Forum: Mathematics
Topic: On taking notes at university
Replies: 11
Views: 2069

Re: On taking notes at university

Try to make as little notes as you can. If you can, read the relevant sections from your course book prior to the lecture, and then only take notes during the lecture about things that weren't in the book, or that you didn't already know. I've found that slavishly taking notes during lectures reduce...
by Torn Apart By Dingos
Sat Nov 14, 2009 11:31 am UTC
Forum: Mathematics
Topic: Best sounding integer sequence
Replies: 6
Views: 1952

Re: Best sounding integer sequence

Related: logic proofs turned into music. These sound rather good, actually.
by Torn Apart By Dingos
Mon Oct 19, 2009 8:01 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 485413

Re: Favorite math jokes

I'd write it as \forall B: \text{span}(B)=\text{you}, |B|=\dim(\text{you})\Rightarrow B\in\text{us}. (Base/basis, tomato/potato) Regarding funny math jokes: perhaps the question should not be "do they exist?", but rather "are they unique?". (I did not come up with...
by Torn Apart By Dingos
Fri Oct 02, 2009 9:41 am UTC
Forum: Mathematics
Topic: which asshat came up with infix?
Replies: 23
Views: 3312

Re: which asshat came up with infix?

I used to believe I only found infix easier to parse than prefix/postfix because I was more used to the former. But now I think infix is actually better. It's convenient that a large expression like ab^{c}\sin x+\frac{xy^2z}{1+z^2} is split in two by the plus sign, so you can easily tell the terms a...
by Torn Apart By Dingos
Tue Aug 04, 2009 10:19 pm UTC
Forum: Mathematics
Topic: Math notation question: "next step" in proofs
Replies: 18
Views: 2502

Re: Math notation question: "next step" in proofs

I'd just use an implication arrow between each step.
by Torn Apart By Dingos
Tue Aug 04, 2009 4:19 pm UTC
Forum: Mathematics
Topic: Math notation question: "next step" in proofs
Replies: 18
Views: 2502

Re: Math notation question: "next step" in proofs

", so" is the same thing as implies, if I understood your first post correctly. Could you give an example of what you mean? Do you mean something like the following? Re(z)=1 Im(z)=2 So z=1+2i I would write that on one line as "Re(z)=1 and Im(z)=2, so z=1+2i". Or possibly (with th...
by Torn Apart By Dingos
Sun Aug 02, 2009 8:22 pm UTC
Forum: Mathematics
Topic: Project euler math/cs education wiki?
Replies: 6
Views: 1589

Re: Project euler math/cs education wiki?

The solutions shouldn't be given away. But when you've solved a problem, you can access a forum where people post their code and solutions.

Wow, I just went to the Project Euler page now. I hadn't been there in a while. There are twice as many problems now as when I last was there.
by Torn Apart By Dingos
Wed Jul 22, 2009 12:50 pm UTC
Forum: Mathematics
Topic: Folding shapes
Replies: 10
Views: 1462

Re: Folding shapes

You want to deform a shape with no volume to a shape with nonzero volume. If you do it homeomorphically, i.e. you deform it continuously, and it can be deformed continuously back to its original shape, this cannot be done. Apropos space-filling curves: all space-filling curves intersect themselves,...
by Torn Apart By Dingos
Wed Jul 22, 2009 11:52 am UTC
Forum: Mathematics
Topic: Infinite reciprocals addition
Replies: 15
Views: 1556

Re: Infinite reciprocals addition

Ok, I'm trying to find a closed form of the sum of the reciprocals of the squares of the primes... And I got to the point of it equaling pi^2/6-1-(pi^2/6-1)(1/2^2 + 1/3^2(1-1/2^2) + 1/5^2(1-1/3^2(1-1/2^2)) + 1/7^2(1-1/5^2(1-1/3^2(1-1/2^2))) + ...) So I need help on finding out what 1/2^2 + 1/3^2(1-...
by Torn Apart By Dingos
Tue Jul 21, 2009 11:36 am UTC
Forum: Mathematics
Topic: Palindromic numbers
Replies: 17
Views: 2295

Re: Palindromic numbers

Are there any numbers that are palindromes in base 2 and base 3? (other than 1) I haven't got the programming skill to run a large check, but I've checked the numbers <1000 by hand and couldn't find any. Yes. http://www.research.att.com/~njas/sequences/?q=6643,+1422773&language=english&go=S...
by Torn Apart By Dingos
Mon Jul 20, 2009 7:23 pm UTC
Forum: Mathematics
Topic: Infinite reciprocals addition
Replies: 15
Views: 1556

Re: Infinite reciprocals addition

This is the harmonic series. If you keep adding terms, you can make it larger than any given integer. The phrase you're looking for is "diverges to infinity". There's a bunch of proofs on the wikipedia page: http://en.wikipedia.org/wiki/Harmonic_series
by Torn Apart By Dingos
Tue Jul 14, 2009 1:01 am UTC
Forum: Mathematics
Topic: Post your interesting/challenging/fun integrals
Replies: 53
Views: 9531

Re: Post your interesting/challenging/fun integrals

csrjjsmp wrote:One of my favorites:
[math]\int_0^1(1-x^7)^{1/5} - (1-x^5)^{1/7}dx[/math]

I assume this is supposed to be 0. Why?
by Torn Apart By Dingos
Sun Jul 12, 2009 4:51 pm UTC
Forum: Mathematics
Topic: Post your interesting/challenging/fun integrals
Replies: 53
Views: 9531

Re: Post your interesting/challenging/fun integrals

This is a classic: 4) \int_{-\infty}^\infty e^{-x^2} dx This is the Gaussian integral. The really clever calculation can be found on Wikipedia, so I won't repeat it here. Regarding 1): It can also be done by equating it with the real part of \int e^x e^{ix} dx . One needs some complex analysis t...
by Torn Apart By Dingos
Wed Jul 08, 2009 10:13 pm UTC
Forum: Mathematics
Topic: Your favourite calculator
Replies: 43
Views: 5638

Re: Your favourite calculator

jroelofs wrote:Can anyone think of anything else that the 84 does that an 89 can't?

I don't know about the 84, but the 83 plots way faster than the 89 Titanium, which really annoys me.
by Torn Apart By Dingos
Mon Jul 06, 2009 2:59 pm UTC
Forum: Mathematics
Topic: multivariable limit
Replies: 11
Views: 2067

Re: multivariable limit

Sure. If the limit doesn't exist, we can a sequence of points heading off to wherever we're taking the limit so that the limit along that sequence of points doesn't exist. Now just connect them with a curve. Clever. Can we get a differentiable curve though (and if yes, what about analytic? :))? We ...
by Torn Apart By Dingos
Mon Jul 06, 2009 10:08 am UTC
Forum: Mathematics
Topic: Examples of vectors
Replies: 16
Views: 1934

Re: Examples of vectors

I'll try to intuitively explain why number sequences and functions can be viewed as vectors. The concept of a vector space of geometric vectors in space ("arrows" pointing from the origin to some point) is the intuitive picture you should keep in your head. If we represent those vectors by...
by Torn Apart By Dingos
Sun Jul 05, 2009 4:46 pm UTC
Forum: Mathematics
Topic: Math crossroads: which course?
Replies: 10
Views: 1426

Re: Math crossroads: which course?

Symbolic math software make all kinds of assumptions. I think both Mathematica and Maple will output 0 if you ask it what \frac d{dx}\frac{df}{dy}-\frac d{dy}\frac{df}{dx} is, even if you provide it with an explicit counterexample f. I've also noticed stuff like getting 0 from 0^x, where x is a vari...
by Torn Apart By Dingos
Sun Jul 05, 2009 2:19 pm UTC
Forum: Mathematics
Topic: multivariable limit
Replies: 11
Views: 2067

Re: multivariable limit

Is it sufficient for the limit to be the same along all continuous curves for the actual limit to exist (by the epsilon delta definition)? If yes, what about differentiable curves? I haven't thought about this, so it might be very easy to answer.
by Torn Apart By Dingos
Mon Jun 29, 2009 7:35 pm UTC
Forum: General
Topic: The Awkwardness Repository
Replies: 23
Views: 2815

Re: The Awkwardness Repository

I win the watch-a-sexually-explicit-movie-with-your-family category. I saw Irreversible with my mother and grandmother. Awkward. I also recently saw Antichrist with my sister. I've seen Borat and Monster's Ball with my mother. Not awkward at all. I remember feeling uncomfortable seeing the sex scene...
by Torn Apart By Dingos
Mon Jun 22, 2009 9:17 am UTC
Forum: Mathematics
Topic: Analysis Help!
Replies: 16
Views: 1325

Re: Analysis Help!

I need to sleep so maybe I'm missing something obvious, but how does f(b)-f(a) \geq 0 imply nondecreasing? Couldn't it still oscillate around between those two endpoints? If the property is satisfied for the interval [a,b], it's satisfied for all subintervals [a',b'] with a<a'<b'<b....
by Torn Apart By Dingos
Sun May 17, 2009 10:06 am UTC
Forum: General
Topic: Picking A Screenname
Replies: 46
Views: 4101

Re: Picking A Screenname

Don't make my mistake. My name sucks. :) I actually registered on these fora with my usual screenname (which I don't hate), but I never got a registration email, and I couldn't re-register, so I had to make something up on the spot, and I got this shitty name. Nowadays though I use my real name as a...
by Torn Apart By Dingos
Sat Apr 25, 2009 7:59 am UTC
Forum: Mathematics
Topic: My question might annoy those who know the answer
Replies: 13
Views: 1371

Re: My question might annoy those who know the answer

This is an ill-defined question. How do you define the ratio of sizes of two sets? You should probably specify a measure. If you use the most natural measure, the Lebesgue measure, on the set of rational numbers and the set of real numbers, you'll get that the ratio is exactly 0. But that is specifi...
by Torn Apart By Dingos
Thu Apr 16, 2009 3:38 pm UTC
Forum: Mathematics
Topic: Analysis question involving uncountable sets
Replies: 16
Views: 2726

Re: Analysis question involving uncountable sets

There must be an integer n>0 such that f(x)>1/n for infinitely many x in A, or else A would be at most countable (can you see this?). So the sum contains infinitely many terms at least as large as 1/n, so it must be infinite.
by Torn Apart By Dingos
Fri Mar 27, 2009 11:08 pm UTC
Forum: Mathematics
Topic: Slowest convergent series
Replies: 4
Views: 1961

Slowest convergent series

The harmonic series \sum 1/n is a "slowest divergent series" in the sense that \sum_{n=1}^\infty\frac1{n^{1+\varepsilon}} is convergent if and only if \varepsilon>0 . Is there a "slowest convergent series" in the sense that there is a function f such that \sum_{n=1}^\infty f(...
by Torn Apart By Dingos
Thu Mar 26, 2009 9:44 pm UTC
Forum: Mathematics
Topic: Nice graphs?
Replies: 19
Views: 6141

Re: Nice graphs?

I created the following graphs by accident (or, if you will, a mad experiment?!). Quothing myself: (From this thread: http://forums.xkcd.com/viewtopic.php?f=3&t=3366&p=66875&hilit=bat+curve#p66875 ) My first try was x=cos(t), y=sin(t)+cos(t)sin(1/cos(t)): http://pici.se/pictures/QTevp9.p...
by Torn Apart By Dingos
Sat Mar 21, 2009 5:51 pm UTC
Forum: Mathematics
Topic: Uncountably many vertical asymptotes?
Replies: 18
Views: 2096

Re: Uncountably many vertical asymptotes?

Then you've just found uncountably many disjoint open intervals in R , which is impossible. Is it not possible for a "uncountable" series with positive terms to converge? No. If you have uncountably many terms, infinitely many of them must be larger than 1/n for some n (or else you would ...
by Torn Apart By Dingos
Sat Mar 07, 2009 12:27 pm UTC
Forum: Mathematics
Topic: dexa- rotation of mathematical proportion/equations
Replies: 7
Views: 1259

Re: dexa- rotation of mathematical proportion/equations

cameronv wrote:I have proven this by inverse mathematics, but need you mathematicians to verify this by linear mathematics.

Can you please share your inverse mathematics proof?
by Torn Apart By Dingos
Wed Mar 04, 2009 11:30 am UTC
Forum: Mathematics
Topic: Tips on handwriting maths?
Replies: 21
Views: 3039

Re: Tips on handwriting maths?

I write ~ for proportionality instead of the symbol that almost looks like an alpha. I have difficulty telling apart \vartheta, \nu, \upsilon, v (vartheta, nu, upsilon, v). I treat the first three as the same letter, and write them all as vartheta. I'm pretty good at writing zeta, but small xi is st...
by Torn Apart By Dingos
Tue Mar 03, 2009 10:41 am UTC
Forum: Mathematics
Topic: Continuum-many Q-linearly indepedent real numbers
Replies: 5
Views: 896

Re: Continuum-many Q-linearly indepedent real numbers

For example, if you know (aleph 0)*A = A for any infinite cardinal A, that would do it. Alternatively, if you prove A n = A for any natural n, you'll be fine. These facts are pretty easy to prove. Can you please prove these? I can prove them for A=N, 2^N, 2^2^N, ..., but not for general sets (N is ...
by Torn Apart By Dingos
Sat Feb 28, 2009 9:49 pm UTC
Forum: Mathematics
Topic: Homework help, Banach spaces...
Replies: 6
Views: 759

Re: Homework help, Banach spaces...

Well, actually, there are lots of limits (in the space of all square integrable functions). You would need to show that they are all discontinuous.
by Torn Apart By Dingos
Sat Feb 28, 2009 6:47 pm UTC
Forum: Mathematics
Topic: Homework help, Banach spaces...
Replies: 6
Views: 759

Re: Homework help, Banach spaces...

Try to think of a sequence of continuous functions such that f_n(x) tends to 0 for x in [0,1) and f_n(x) tends to 1 for x in [1,2].
by Torn Apart By Dingos
Tue Feb 24, 2009 4:13 pm UTC
Forum: Mathematics
Topic: Calculating Sine
Replies: 4
Views: 745

Re: Calculating Sine

A simple, accurate and efficient method is to use a recurrence relation that halves the argument repeatedly (e.g. \cos(x)=2\cos^2(x/2)-1 ) until the argument is so small that a MacLaurin expansion is very accurate (e.g. \cos(x)\approx 1-x^2/2 ). With my example you can calcul...
by Torn Apart By Dingos
Tue Feb 24, 2009 10:49 am UTC
Forum: Mathematics
Topic: vegetarianism, insults and a very silly problem
Replies: 16
Views: 2282

Re: vegetarianism, insults and a very silly problem

That's pretty easy to counter. For every meat dish you eat, I'll eat a vegetarian dish. You'll get full faster than I will, and I will win.
by Torn Apart By Dingos
Tue Feb 24, 2009 10:43 am UTC
Forum: Mathematics
Topic: Function on the line
Replies: 2
Views: 420

Re: Function on the line

Presumably the real line, i.e. the real numbers. So a function on the line is a function [imath]f:\mathbb R\to\mathbb R[/imath].
by Torn Apart By Dingos
Mon Feb 23, 2009 8:22 pm UTC
Forum: Mathematics
Topic: vegetarianism, insults and a very silly problem
Replies: 16
Views: 2282

Re: vegetarianism, insults and a very silly problem

How about we just conclude that Maddox is an idiot?

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