Search found 209 matches

by aguacate
Thu Feb 21, 2008 11:52 pm UTC
Forum: Mathematics
Topic: Sin(q*pi)=r; q,r rational
Replies: 7
Views: 1866

Sin(q*pi)=r; q,r rational

I got started on this problem while traveling down on a tangent to my algebra homework. Let Q be the rationals and R be the reals. Define f:Q->R by f(q)=Cos(q*pi). How many elements are in f(Q) \cap Q? (by \cap I mean intersect). edit: Yes I did mean "f(Q) \cap Q" and not "f(Q) \cap R...
by aguacate
Thu Jan 24, 2008 2:12 am UTC
Forum: Mathematics
Topic: Calculating Frenet triples in mathematica
Replies: 2
Views: 1228

Calculating Frenet triples in mathematica

Does anyone know if mathematica can calculate the curvature and torsion of a vector function? I would like to double check my geometry homework.
by aguacate
Thu Jan 10, 2008 5:39 pm UTC
Forum: Mathematics
Topic: Math bloopers heard in math classes
Replies: 252
Views: 35225

Re: Math bloopers heard in math classes

The worst math teacher I ever had (first day of class):a meter is a different length in the evening then it is in the morning Me:*headache* Teacher:this is because in the evening the meter stick is warmer, and expands slightly. Me:<explanation of how the meter is defined as the distance light goes ...
by aguacate
Wed Jan 09, 2008 2:11 am UTC
Forum: Language/Linguistics
Topic: Whence and hence
Replies: 19
Views: 6743

Re: Whence and hence

OK, I think I've got it. If you make statement P and wish to smoothly statement Q, an implication of P, then you use "whence". Example: "All prime numbers greater than 2 are odd, whence 22 is not prime." Hence on the other hand is used to start a statement, and if I wished to emp...
by aguacate
Mon Jan 07, 2008 7:20 pm UTC
Forum: Language/Linguistics
Topic: Whence and hence
Replies: 19
Views: 6743

Whence and hence

My algebra teacher uses whence a lot where I would have expected him to use hence. He is always mentioning word histories as new words get brought up in lectures and in his speech it is obvious that he tries consciously to use a very precise vocabulary, so I can only assume he picks whence over henc...
by aguacate
Wed Jan 02, 2008 8:33 pm UTC
Forum: Mathematics
Topic: Division by Zero (Please, no new threads about this)
Replies: 367
Views: 84393

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

Why so much hate? Learning what is not true is just as important as learning what is true.

After all, Q is our general field, R is just one of many completions. Shouldn't this be discussed(if at all) in Q?


Isn't the completion of Q unique?
by aguacate
Sun Dec 30, 2007 10:44 pm UTC
Forum: Mathematics
Topic: Urysohn lemma
Replies: 5
Views: 1475

Re: Urysohn lemma

Maybe I just didn't get the obviousness of the rest of the proofs in my topology course, so this one didn't seem like it was on a totally different level. That course kicked my ass. Although my teacher kept telling us that the the proofs were all trivial and the definitions made the class hard. Mayb...
by aguacate
Sun Dec 30, 2007 10:02 pm UTC
Forum: Mathematics
Topic: Urysohn lemma
Replies: 5
Views: 1475

Urysohn lemma

In my topology book by Munkres, the Urysohn lemma is described as "the first deep theorem of the book" because its proof involves a very original idea that very very few people could come up with on their own. I am a little self conscious on my basic proof skills and I feel like it is some...
by aguacate
Sun Dec 30, 2007 12:37 am UTC
Forum: Mathematics
Topic: Division by Zero (Please, no new threads about this)
Replies: 367
Views: 84393

Re: 0/0 = {R} U {I} ?

No, sorry but you are not correct. First off its not "undefined" its "indeterminate" Say 0*x=0 therefore 0/0=x if it wasn't indeterminate. But isn't there another number a not equal to x such that 0*a=0 therefore a=x, which is a contradiction. Also, x/0=undefined and 0/x = 0 if ...
by aguacate
Sat Dec 15, 2007 5:34 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 488413

Re: Favorite math jokes

Ended wrote:(from here)


Q: Do you know any catchy anagram of Banach-Tarski?
A: Banach-Tarski Banach-Tarski
by aguacate
Mon Dec 10, 2007 2:54 am UTC
Forum: Mathematics
Topic: Amusing answers to tests
Replies: 393
Views: 60532

Re: Amusing answers to tests

A friend's answer for the chemistry exam the week before last. The question was something along the lines of You are a hydrogen molecule in a balloon filled with equal moles of hydrogen and oxygen molecules at 2 atm pressure. A student ignites the balloon with a match. Describe: 1) What you see ini...
by aguacate
Sun Dec 02, 2007 1:47 am UTC
Forum: Mathematics
Topic: Favourite Field of Math?
Replies: 60
Views: 5391

Re: Favourite Field of Math?

This has been my experience so far: in Calculus you learn how to calculate things (like derivatives, integrals, areas, volumes, limits, etc.); whereas in Analysis, you learn how to prove things. I guess you could say the difference is in rigor. Or else you could say one is learning how to use the to...
by aguacate
Thu Nov 29, 2007 9:51 pm UTC
Forum: Mathematics
Topic: What proofs are (split from amusing test answers)
Replies: 37
Views: 3936

Re: What proofs are (split from amusing test answers)

I think the question is not "Are the logical rules of inference true?". Nor is it "Are these postulates true?". But rather "Do these rules model how we think well?" and "Are these postulates good models for our intuitive idea of the object at hand?" I don't th...
by aguacate
Fri Nov 23, 2007 6:29 am UTC
Forum: Mathematics
Topic: Favourite Erroneous "Proofs"
Replies: 194
Views: 43426

Re: Favourite Erroneous "Proofs"

If a relation is symmetric and transitive, then it is also reflexive. (I came up with this one myself during a lecture today, I was quite proud) a R b, b R c -> a R c that is transitivity. let c=a. a R b, b R a -> a R a since the first half of that proposition is true for a symmetric R , we can be ...
by aguacate
Thu Nov 22, 2007 8:32 pm UTC
Forum: Mathematics
Topic: Uh oh. My math teacher says .999... does not equal 1.
Replies: 9
Views: 3943

Re: Uh oh. My math teacher says .999... does not equal 1.

Yeah, IVT has to do with functions... what function was even mentioned??

What the teacher is incorrectly trying to apply is the fact that the real numbers are dense. That is, every number in the set of the real numbers is a limit point.
by aguacate
Wed Nov 21, 2007 8:29 am UTC
Forum: Mathematics
Topic: Fluency with mathematical proofs.
Replies: 18
Views: 3065

Re: Fluency with mathematical proofs.

I second the buying your intro to abstract math book early. I read (here I think - there is an older thread about reading proofs that I couldn't find after a quick search) that papers written by John Conway are good for beginners because they are easy to understand. Haven't checked his stuff out bey...
by aguacate
Mon Nov 19, 2007 12:33 am UTC
Forum: Mathematics
Topic: sylow subgroups
Replies: 15
Views: 2510

Re: sylow subgroups

if qx is not congruent to 1 mod p, for all 0<x<b
by aguacate
Sun Nov 18, 2007 6:40 am UTC
Forum: Mathematics
Topic: Amusing answers to tests
Replies: 393
Views: 60532

Re: Amusing answers to tests

Once my friend and I turned in our weekly notebook photocopies for our electical engineering class late. As a way of reconciling with the TA, I put a $5 bill on the title page, but I did it pre-photocopy.

Yeah, it was funnier at the time...
by aguacate
Sat Nov 17, 2007 4:10 am UTC
Forum: Mathematics
Topic: sylow subgroups
Replies: 15
Views: 2510

Re: sylow subgroups

btilly - nice. I guess I don't see how (3456) generates the other cycles though. I haven't slept in a while.

Guess: is it because of the inverses? I don't have a solid understanding of what inverses look like yet.
by aguacate
Fri Nov 16, 2007 11:43 pm UTC
Forum: Mathematics
Topic: Fast-tracking mathematics.
Replies: 55
Views: 4754

Re: Fast-tracking mathematics.

All I have to offer is advice: There is no substitute for treadging through the boring classes. You might be able to pick up the ideas and the basics, and even pass any test that you would have to pass in the boring classes, but it's not the same. If you want to go far in a subject (and I guess this...
by aguacate
Fri Nov 16, 2007 11:33 pm UTC
Forum: Mathematics
Topic: sylow subgroups
Replies: 15
Views: 2510

sylow subgroups

Just had my algebra midterm, things went well, except I couldn't figure this one out: Find a 2-Sylow subgroup of the symmetric group on 6 letters, S 6 . I had no idea how to approach this, so with nothing to lose that I wouldn't lose anyway by leaving the answer blank, I started with (14), (25), (36...
by aguacate
Tue Nov 13, 2007 12:24 am UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14132

Re: Proficiency with LaTeX

How do you write out a multi-part function?
by aguacate
Sat Nov 10, 2007 7:50 am UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4222

Re: On Linear Algebra

For everyone who says you don't need any calculus to do linear algebra, have you ever heard of the wronskian? Not only did I cover it in my linear algebra class, but the students I tutor are learning it, at a separate university, in their linear algebra class. Admittedly it's not that major of a top...
by aguacate
Thu Nov 08, 2007 4:35 pm UTC
Forum: Mathematics
Topic: Proof by contradiction is never needed!
Replies: 22
Views: 2821

Re: Proof by contradiction is never needed!

What about the proof that sqrt(2) is irrational? The direct statement would presumably be: (x^2 = 2) => (x is irrational) So the contrapositive would be that: (x is rational) => (x^2 =/= 2) This doesn't seem (to me) easy to do without contradiction somewhere. x=n/d => n^2 has an even number of 2s i...
by aguacate
Tue Nov 06, 2007 7:47 pm UTC
Forum: Mathematics
Topic: series and limsups
Replies: 1
Views: 845

series and limsups

The official ratio and root tests use the limsup of a n and not just the lim. On the other hand if lim a n converges, then limsup=liminf=lim. But then if a series converges, then lim a n must not only converge, but converge to 0. So, why limsup? ... OK, actually I just realized while typing this tha...
by aguacate
Thu Nov 01, 2007 4:58 am UTC
Forum: Mathematics
Topic: Inverting Laplace Transforms
Replies: 6
Views: 1538

Re: Inverting Laplace Transforms

All I know is that laplace transforms kicked ass when I was analyzing circuits. I vaguely remember that multiplication in the laplace domain was addition in the time domain. So the inverse of F(s) would work out to be

L-1(e-2s)+L-1(2/s2-4)
by aguacate
Sat Oct 27, 2007 4:45 am UTC
Forum: Mathematics
Topic: Ways of making a team
Replies: 3
Views: 1112

Re: Ways of making a team

One way to do it is:

5C4 + (5C3*5C1) + (5C2*5C2) + (5C1*5C3)

where aCb is "a choose b" or a!/[(a-b)!*b!]. So it's:

5!/4! + 2*5!*5!/(4!*2!*3!) + [5!/(3!*2!)]^2

5 + 14400/144 + (120/12)^2

5 + 100 + 100

= 205


What is your method trying to do? Where did your numbers come from?
by aguacate
Fri Oct 26, 2007 4:24 am UTC
Forum: Mathematics
Topic: cantor set = set of all what in base 3?
Replies: 3
Views: 1220

cantor set = set of all what in base 3?

Reading through my notes in my Real Analysis class, I wrote down that the cantor set P = {x \in \R | x has n 1s in its base three expansion}. I guess I forgot to put what n was. Is n any element of Z? Did I mean to write 'inf'? Little help please?
by aguacate
Thu Oct 25, 2007 7:23 pm UTC
Forum: Mathematics
Topic: Halp at Toplogy!
Replies: 10
Views: 1431

Re: Halp at Toplogy!

I see what you are saying, and I think the last two questions are indeed equivalent. Yes, you cannot take the union of all the elements of a basis without covering S. OK wait stop. One of the possibly confusing points of topology is that a topological space consists of TWO sets. Here I am going to u...
by aguacate
Thu Oct 25, 2007 4:45 am UTC
Forum: Mathematics
Topic: Halp at Toplogy!
Replies: 10
Views: 1431

Re: Halp at Toplogy!

But that is the usual definition, n'est pas? Nope. First of all, in the usual definition, the basis has to cover S, not just be able to create all open sets by union. This is a necessary condition for S to be made up of a union of elements of the basis. If the basis did not cover S, then arbitrary ...
by aguacate
Thu Oct 25, 2007 12:50 am UTC
Forum: Mathematics
Topic: Math movies
Replies: 34
Views: 3928

Re: Math movies

23 was awesome I thought. It gave me nightmares

edit: "The Number 23" I guess
by aguacate
Mon Oct 22, 2007 11:52 pm UTC
Forum: Mathematics
Topic: Spanish help
Replies: 14
Views: 2523

Re: Spanish help

Topology -> topología Set -> conjunto Complex number -> número complejo field -> campo metric space -> espacio métrico theorem -> teorema prove -> demostrar proof -> demostración element -> elemento region -> región La próxima vez vete a un foro hispanohablante ;-) [next time go to a spanish-speaki...
by aguacate
Sun Oct 21, 2007 9:40 pm UTC
Forum: Mathematics
Topic: Spanish help
Replies: 14
Views: 2523

Re: Spanish help

Did you try what I said in my PM? Yeah, so the suggestion was to look it up in wikipedia then change the language for that article to spanish. To be honest, I haven't tried it yet, but it sounds like a good idea. ... OK I just tried it, and since the axiom of choice wasn't in any of the other place...
by aguacate
Sun Oct 21, 2007 5:47 pm UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14132

Re: Proficiency with LaTeX

Has anyone found a nice way to title homework assignments? I kind of want to use \maketitle, just because it's there and it makes so much sense, but is there a way of toning it down a little so it fits more the style of "just another assignment"? Use the report document type? Even worse -...
by aguacate
Sun Oct 21, 2007 4:37 am UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14132

Re: Proficiency with LaTeX

Has anyone found a nice way to title homework assignments? I kind of want to use \maketitle, just because it's there and it makes so much sense, but is there a way of toning it down a little so it fits more the style of "just another assignment"?
by aguacate
Sat Oct 20, 2007 11:59 pm UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14132

Re: Proficiency with LaTeX

Does anyone know how to apply a condition underneath a large union? For instance the union of B_{alpha} over a collection alpha. Like this http://upload.wikimedia.org/math/1/4/f/14ff2c1ffddc8472a030c5ad6f6ebc5f.png ? If so then \bigcap_{\alpha \in A} B_\alpha Thanks! It seems like it only works in ...
by aguacate
Sat Oct 20, 2007 10:28 pm UTC
Forum: Mathematics
Topic: Proficiency with LaTeX
Replies: 86
Views: 14132

Re: Proficiency with LaTeX

Does anyone know how to apply a condition underneath a large union? For instance the union of B_{alpha} over a collection alpha.
by aguacate
Sat Oct 20, 2007 5:43 am UTC
Forum: Mathematics
Topic: Spanish help
Replies: 14
Views: 2523

Spanish help

Como se dicen las siguientes frases en espanol?

Topology
Set
Complex number
field
metric space
theorem
prove
proof
element
region

En cambio, hay algun sitio donde se puede buscar las palabras de las matematicas?
by aguacate
Tue Oct 16, 2007 6:01 pm UTC
Forum: Mathematics
Topic: Are there jordan curves with non-zero area?
Replies: 15
Views: 5510

Re: Are there jordan curves with non-zero area?

http://img146.imageshack.us/img146/6720/96p00523l1ad3.th.gif http://img266.imageshack.us/img266/8526/96p00523l2ws2.th.gif http://img266.imageshack.us/img266/9136/96p00523l4lf0.th.gif http://img266.imageshack.us/img266/4773/96p00523l5kr6.th.gif http://img152.imageshack.us/img152/5084/96p00523l7ij7.t...
by aguacate
Tue Oct 16, 2007 7:46 am UTC
Forum: Mathematics
Topic: Are there jordan curves with non-zero area?
Replies: 15
Views: 5510

Re: Are there jordan curves with non-zero area?

Apparently the answer is yes:

http://links.jstor.org/sici?sici=0002-9947(190301)4%3A1%3C107%3AAJCOPA%3E2.0.CO%3B2-T

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