## Search found 758 matches

Tue May 13, 2014 5:28 pm UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 13147

### Re: Need second opinion. I think I disproved God.

... it's a bit delusional to think any one of them accomplisfes what it claims. Or that it has anything to do with mathematics. Using a proof and calling it math is like using words and calling it poetry. That said, there's not really a board on this forum for a post like this, except maybe SB? I'm...
Tue May 13, 2014 5:44 am UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 13147

### Re: Need second opinion. I think I disproved God.

Yes, this looks correct. Congratulations.
Thu May 08, 2014 5:23 pm UTC
Forum: Mathematics
Topic: Collatz Binary Decision Tree (Much Improved Version)
Replies: 1
Views: 2254

### Re: Collatz Binary Decision Tree (Much Improved Version)

First, you should probably just edit the original post, rather than reposting and then... rethreading? Second, when it comes to mathematical discoveries, there's a ton of stuff that mathematicians "know" but have never actually been bothered to write down, mostly because if you know the te...
Fri Apr 11, 2014 9:42 pm UTC
Forum: Mathematics
Replies: 3
Views: 1990

### Re: Question about Taylor series

Each time you take a derivative, you bring the exponent down in front and subtract one from the exponent. If you differentiate something several times and watch the coefficient as you do it, you'll notice that you deposit n*(n-1)*(n-2)*... out in front of each term. You don't want that to be there, ...
Tue Mar 25, 2014 7:05 pm UTC
Forum: Mathematics
Replies: 20
Views: 4086

The Galois group of Q(sin(π/11), i) = Q(e iπ/11 ) over Q is cyclic of order 10. I haven't done any Galois theory in several years, but I think that means that the Galois group of Q(sin(π/11)) over Q is cyclic of order 5. It does. The Galois group of Q(sin(pi/11),i) over Q(sin(pi/11)) has order 2 si...
Sat Mar 22, 2014 5:23 pm UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 35962

### Re: Axiomatic mathematics has no foundation

What do you mean by the quoted statement below? I'm not trying to be argumentative, I just want a clear explanation of what you mean. If you have any books or papers that touch on the topic, that'd be awesome. Identity relationships really mess with set theory - which is why set theories tend to exc...
Fri Mar 21, 2014 5:21 pm UTC
Forum: Mathematics
Topic: Can a surface be formed by the intersection?
Replies: 7
Views: 2684

### Re: Can a surface be formed by the intersection?

Pictures and equations of the two types of paraboloids jestingrabbit mentions:

http://en.wikipedia.org/wiki/Paraboloid
Fri Mar 21, 2014 5:00 pm UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 35962

### Re: Axiomatic mathematics has no foundation

If you're OK with talking about the "O from which the arrows leave" and distinguishing objects based on their relationships to other objects in a network, then you should be OK with some primitive models of set theory. There's actually some "model" of a very weak set theory where...
Wed Mar 12, 2014 2:32 am UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 14303

### Re: Circularity in Formal Languages?

So I always felt kind of uneasy about this for a long time. It never cleared up until I learned about different models of set theory, via topos theory, but you don't really need to do all that to understand what's going on. What set theory is really trying to do is create a miniature model M of obje...
Sun Mar 09, 2014 1:25 pm UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 35962

### Re: Axiomatic mathematics has no foundation

The difference lies in understanding what is being done. But all mathematicians do understand what's being done. Everybody knows that if you keep deconstructing the meaning of what you're doing, it devolves into nonsense. Mathematicians know that mathematics is not immune to this sort of thing. Whe...
Tue Nov 12, 2013 7:07 am UTC
Forum: Mathematics
Topic: Dogma in Math
Replies: 98
Views: 15005

### Re: Dogma in Math

I don't think you're understanding the purpose of a definition. It doesn't make sense to "stack 5 books in no ways" any more than it makes sense to "multiply 2 by itself negative one-half times". And yet, you probably don't have any problems with the symbols 2^{-\frac{1}{2}} defi...
Tue Nov 12, 2013 1:57 am UTC
Forum: Mathematics
Topic: Capability to do mathematics.
Replies: 7
Views: 2081

### Re: Capability to do mathematics.

My (working) memory is also not all that good. I bet most academics won't claim to have astounding memories. I feel like biological memory works like technological memory. You'll never have enough! I need to sleep on it before I can really answer any abstract questions about the mater. While some s...
Tue Nov 12, 2013 1:44 am UTC
Forum: Mathematics
Topic: Dogma in Math
Replies: 98
Views: 15005

### Re: Dogma in Math

It was a legitimate question wrapped up with some obnoxious statements that I imagine the OP will be embarrassed to have written in 5-6 years. :D I have my fair share of such posts, no doubt... At any rate, if a whole bunch of people tell you that your behavior isn't acceptable in their community, y...
Fri Nov 08, 2013 3:04 am UTC
Forum: Mathematics
Topic: Dogma in Math
Replies: 98
Views: 15005

### Re: Dogma in Math

So what did your program do for n=0? Seems like you should be more upset you didn't think about error checking, rather than what the community of mathematicians have generally agreed upon is a convenient thing to mean when we write 0!. And if your program did indeed error check and didn't spit out 1...
Wed Oct 30, 2013 1:34 am UTC
Forum: Mathematics
Topic: Approximation of pi
Replies: 9
Views: 3070

### Re: Approximation of pi

Since Google says that the first few digits of pi are 3.14159265359 and you didn't post any of your code for us to look at, the only reasonable answer I can think to give you is... no. But I do wonder why it's so far off. What happens for higher value of n?
Mon Sep 23, 2013 3:48 am UTC
Forum: Mathematics
Replies: 3
Views: 1387

### Re: Question about homotopy groups

The homotopy groups of a single 2-sphere aren't known, so I don't know how much progress you'll make computing the homotopy groups of an uncountable wedge of them.
Thu Jul 25, 2013 6:30 pm UTC
Forum: Fictional Science
Topic: Helvetica Scenario
Replies: 21
Views: 114908

### Re: Helvetica Scenario

Relevant part at 6:17

If you click "share", you can select a time that the video will load at when accessed through the link.
Sun Jul 14, 2013 7:45 pm UTC
Forum: General
Topic: I want to learn something
Replies: 31
Views: 10945

### Re: I want to learn something

If you are interested in mathematics, you'll find that there's more mathematics than anyone could possibly learn in lifetime! You'll never be bored! (Unless you find learning and thinking about mathematics boring, in which case you'll be very bored!)
Sun Jul 14, 2013 7:14 pm UTC
Forum: Mathematics
Topic: SIMPLEST PROOF OF FERMAT'S LAST THEOREM
Replies: 45
Views: 12502

### Re: SIMPLEST PROOF OF FERMAT'S LAST THEOREM

I don't. Incoherence isn't novel, and making fun of it stops being fun once you realize that it is often caused by mental illness. Seconded. There's no reason I can think of to keep a thread like this once the poster says something like: You see, no one can come up with a sensible reason why my pro...
Sun Jun 02, 2013 9:31 pm UTC
Forum: Mathematics
Topic: Question about factoring homogeneous polynomials
Replies: 4
Views: 4896

### Re: Question about factoring homogeneous polynomials

No problem. And you're certainly not worthless. Algebraic geometry is really, really hard.
Sun Jun 02, 2013 8:29 pm UTC
Forum: Mathematics
Topic: Question about factoring homogeneous polynomials
Replies: 4
Views: 4896

### Re: Question about factoring homogeneous polynomials

Think about it geometrically. If f(x,y) is homogeneous of degree k, we can imagine its variety sitting in projective space. We want to show that the polynomial's variety in affine space contains an affine line, so that amounts to showing the polynomial has a point on which it vanishes in projective ...
Tue May 28, 2013 2:11 am UTC
Forum: Mathematics
Topic: Origin of e as group identity?
Replies: 7
Views: 2559

### Re: Origin of e as group identity?

It comes from the phrase "Eh, I'll leave you alone."
Thu May 23, 2013 10:18 pm UTC
Forum: Mathematics
Topic: n-dimension rotation: Data rotation
Replies: 4
Views: 2227

### Re: n-dimension rotation: Data rotation

You need to define closer, and what aspects of the data you want to be preserved under the transformation.
Tue May 07, 2013 4:37 am UTC
Forum: Mathematics
Topic: 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1*0
Replies: 28
Views: 6419

### Re: 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1*0

Sort of repeating what's been said above: None of the axioms of the real numbers have anything to do with preference of operations. They define an object. The expressions we write down to stand for variables and constants in that object are completely separate from that object. \mathbb{R} does not c...
Thu May 02, 2013 6:11 am UTC
Forum: Mathematics
Topic: Does this have a name? (3d complex numbers)
Replies: 14
Views: 4166

### Re: Does this have a name? (3d complex numbers)

There are actually theorems about associative real division algebras. They're all even dimensional, I believe. For your system, since you have i^4 = 1 = ij , then i^3 = j , and you're correct in saying your object is a field, since it's actually just \mathbb{C} . You could admittedly say you want so...
Fri Apr 26, 2013 11:40 am UTC
Forum: Mathematics
Topic: Module intuition
Replies: 7
Views: 2903

### Re: Module intuition

So my advice, which is worth exactly what you paid for it, is not to look for intuition. Instead, go through every example of a module you can think of, and work with it until the notion of a "module" becomes second nature. I've found this is sound advice for learning any mathematics. Thi...
Tue Apr 23, 2013 12:42 pm UTC
Forum: Mathematics
Topic: Module intuition
Replies: 7
Views: 2903

### Re: Module intuition

Your intuition for rings carries over. We want to make all the elements of the submodule "the same", and we do this in a way that works well with the algebra, so the remaining object is still a module. Think about vector spaces, maybe R^3. If I pick a vector subspace V (which is precisely ...
Mon Apr 15, 2013 11:39 pm UTC
Forum: Mathematics
Topic: Divergent Series
Replies: 12
Views: 4667

### Re: Divergent Series

Try thinking about the reverse problem. Begin by a nice linear relation, say: S = 2 + 5S Now, start expanding, substituting S in for itself each time: S = 2 + 5(2 + 3S) = 2 + 10 + 25S = 2 + 10 + 25(2 + 3S) = 2 + 10 + 50 + 125S and we can spot how the formula unwinds itself. At the nth iteration, it ...
Thu Apr 11, 2013 10:28 am UTC
Forum: Mathematics
Topic: n-dimensional complex vector rotation matrix
Replies: 2
Views: 1255

### Re: n-dimensional complex vector rotation matrix

The easiest way I can think to construct the rotation matrix is to choose a nice basis. If I want vector A parallel to vector B, then normalize A to get a unit vector a. Normalize B to get a unit vector b. From that, construct an orthonormal basis by the Gram-Schmidt process, and then create a matri...
Fri Apr 05, 2013 1:48 am UTC
Forum: Mathematics
Topic: Probabilities with Ω={}
Replies: 12
Views: 2630

### Re: Probabilities with Ω={}

If X is the empty set, then X and X are disjoint (just try and look for an element in the intersection...), and so the probability P(X or X) = P(X) + P(X) = 1 + 1 = 2. But X or X is X, since... it's the empty set. So we get 1 = 2. I don't see a way to make sense of the probability with an empty even...
Sat Mar 09, 2013 7:13 pm UTC
Forum: Mathematics
Topic: Question to resolve feud with math teacher
Replies: 2
Views: 1545

### Re: Question to resolve feud with math teacher

If you want to write up a different solution, the following might be useful:

http://en.wikipedia.org/wiki/Dirichlet's_approximation_theorem
Sun Mar 03, 2013 11:59 pm UTC
Forum: Mathematics
Topic: Discontinituous increasing function?
Replies: 20
Views: 3982

### Re: Discontinituous increasing function?

Yup. But remember that countable dense subsets exist, and we can add up a countable number of things and get a finite number. This is sort of a hint on how to construct such a function.
Thu Feb 28, 2013 6:04 am UTC
Forum: Mathematics
Topic: Infinite Sets
Replies: 18
Views: 3523

### Re: Infinite Sets

Just scroll down the page a bit. The set you constructed doesn't violate regularity, but it implies the existence of a set that does.
Wed Feb 27, 2013 10:53 pm UTC
Forum: Mathematics
Topic: Infinite Sets
Replies: 18
Views: 3523

### Re: Infinite Sets

There's actually a set theory in which you demand such "not well founded" sets exist. You drop the Foundation Axiom from ZFC and add the Antifoundation Axiom, which states that every graph corresponds to sets such that the arrows correspond to containment. For instance, the graph of one no...
Mon Feb 25, 2013 2:04 am UTC
Forum: Mathematics
Topic: Help with Principles of Mathematical Analysis
Replies: 11
Views: 3137

### Re: Help with Principles of Mathematical Analysis

Just a bit of advice. There are lots of people that will disagree with me on this, but... Rudin is an abhorrently bad book to learn analysis out of for the first time. Absolutely terrible. It's wonderful if you already have exposure to analysis and are going through it a second time to flesh out wha...
Wed Feb 13, 2013 5:08 am UTC
Forum: Mathematics
Topic: Derivative of lnx^2
Replies: 3
Views: 6111

### Re: Derivative of lnx^2

Your book is wrong. If you don't believe me:

http://www.wolframalpha.com/input/?i=di ... 28x%5E2%29
Mon Feb 11, 2013 10:14 am UTC
Forum: Mathematics
Topic: Method for finding eigenplanes of a linear transformation.
Replies: 2
Views: 1373

### Re: Method for finding eigenplanes of a linear transformatio

Jordan Canonical Form is what you're looking for. It basically gives you a decomposition of the vector space into invariant subspaces. If you don't like complex numbers, scroll down to the "real matrix" section to see what happens in that case. In the theory that gives you that decomposit...
Tue Oct 16, 2012 3:34 pm UTC
Forum: Mathematics
Topic: What course to take next?
Replies: 7
Views: 1858

### Re: What course to take next?

As mentioned before, elementary group/ring theory and linear algebra offers a good selection of basic proofs to help with thinking in a mathematically rigorous fashion. I typically advise against studying point set topology until some sort of introduction to analysis. I imagine that the ideas in top...
Tue Oct 02, 2012 3:20 am UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 92956

### Re: "Oh no! We forgot how to say... math... stuff!"

I would take that to mean that the domain of the map is V.
Sat Sep 29, 2012 11:13 pm UTC
Forum: Mathematics
Topic: Linear Algebra Homework: Annihilators, Isomorphisms
Replies: 4
Views: 2588

### Re: Linear Algebra Homework: Annihilators, Isomorphisms

That looks right. Of course, be careful and make sure you include the little details, like well-definedness of f, in your proof.