## Search found 849 matches

- Thu Oct 17, 2013 1:26 pm UTC
- Forum: Mathematics
- Topic: Substitution systems
- Replies:
**6** - Views:
**2446**

### Re: Substitution systems

I'm still a little confused as you haven't given a definition, just an example. If you have two rules, does one get precedence over the other? Do you start scanning from left to right until you meet an instance that a rule can be applied and then go back to the start or do you carry on to the end ap...

- Tue Oct 15, 2013 2:53 pm UTC
- Forum: Mathematics
- Topic: Substitution systems
- Replies:
**6** - Views:
**2446**

### Re: Substitution systems

This sounds like it may be related to substitution tilings in 1 dimension but it's hard to tell as I don't have the book. Could you give a precise definition of what one of these systems is?

- Mon Sep 23, 2013 1:04 pm UTC
- Forum: Mathematics
- Topic: Question about homotopy groups
- Replies:
**3** - Views:
**1265**

### Re: Question about homotopy groups

You might be able to figure out pi i (X) for a few values of i. Any more seems unlikely. Perhaps the only good news is that really all of the higher homotopy is tied up in the projective plane because the Klein bottle is a K(Z x Z/2Z, 1) and so you may be able to find a formula for pi i (X) for i>1 ...

- Mon Jul 29, 2013 10:55 pm UTC
- Forum: Mathematics
- Topic: Help with proof (or not) in symmetry
- Replies:
**11** - Views:
**4129**

### Re: Help with proof (or not) in symmetry

I'll take a stab at trying to put your ideas in to a more formal setting (as your language isn't very formal, there's a certain amount of guess work that I'll have to do here). For the sake of not using already established language ( discrete dynamical systems already have a definition), we'll call ...

- Sat Mar 16, 2013 6:39 pm UTC
- Forum: Mathematics
- Topic: Inserting a cone into itself?
- Replies:
**11** - Views:
**2229**

### Re: Inserting a cone into itself?

I remember doing something similar with socks when I was younger.

- Fri Mar 01, 2013 5:35 pm UTC
- Forum: Mathematics
- Topic: Connected v. Path-connected
- Replies:
**9** - Views:
**2527**

### Re: Connected v. Path-connected

As to why connectedness is a useful definition. There are a few topological invariants which can pick out the number of connected components of a space but which a similar invariant might be fairly useless because it can only distinguish path-connected components. I'm thinking in particular of Čech ...

- Sun Feb 24, 2013 3:47 pm UTC
- Forum: Mathematics
- Topic: Average number of legs of a person
- Replies:
**2** - Views:
**5102**

### Re: Average number of legs of a person

Very quick googling (http://www.amputee-coalition.org/fact_sheets/amp_stats_cause.html) suggests there are 1.7million amputees in america in a population of roughly 320 million (so roughly 1 in every 200 people has had an amputation). This of course takes in to account upper as well as lower limb lo...

- Sat Feb 23, 2013 3:15 pm UTC
- Forum: Mathematics
- Topic: Complexity of a sequence (combinatorics)
- Replies:
**5** - Views:
**1141**

### Re: Complexity of a sequence (combinatorics)

I had a feeling you might see through the not-very-well-hidden guise of the problem jr :), especially considering the post you wrote a few months ago on my dense geodesic thread. Thanks for the reply, and I think what you're describing is the method Arnoux et al. used to prove that a 3D cutting sequ...

- Fri Feb 22, 2013 6:47 pm UTC
- Forum: Mathematics
- Topic: Complexity of a sequence (combinatorics)
- Replies:
**5** - Views:
**1141**

### Re: Complexity of a sequence (combinatorics)

Yeah ok I should have gotten the first part a lot quicker, it's just (n+m)Cn + (n+m+1)Cn + (n+m+1)C(n+1) + (n+m+2)C(n+1) = 2[(n+m)C(n-1)] + 5[(n+m)Cn] + 2[(n+m)C(n+1)]

- Fri Feb 22, 2013 5:30 pm UTC
- Forum: Mathematics
- Topic: Complexity of a sequence (combinatorics)
- Replies:
**5** - Views:
**1141**

### Complexity of a sequence (combinatorics)

My question comes in two parts. The first should hopefully be fairly easy, the second I'm not sure is even solvable without some sophisticated machinery. Let s be a sequence, in the alphabet {a,b,c} and such that between any two consecutive occurences of a's there are either n or n+1 b's and m or m+...

- Thu Feb 14, 2013 5:41 pm UTC
- Forum: Mathematics
- Topic: A Thread for scratch123's Random Math Questions
- Replies:
**71** - Views:
**15234**

### Re: A Thread for scratch123's Random Math Questions

You can't just start throwing words around like 'simple' without defining them. If you're trying to have a serious mathematical discussion, don't use terms with ambiguous meaning unless you're going to clarrify the specific definition you're using. It does no good to confuse someone because you're u...

- Wed Feb 13, 2013 12:18 pm UTC
- Forum: Mathematics
- Topic: O(n²) difficulty learning further mathematics.
- Replies:
**4** - Views:
**1551**

### Re: O(n²) difficulty learning further mathematics.

It sounds like you might be trying to learn the applicable subjects before gaining a solid foundation. Unfortunately, the way mathematics is structured, you need to learn a fairly large amount of background if you want any chance of being able to understand that kind of stuff. I would suggest trying...

- Mon Feb 11, 2013 12:49 am UTC
- Forum: Mathematics
- Topic: Method for finding eigenplanes of a linear transformation.
- Replies:
**2** - Views:
**1301**

### Method for finding eigenplanes of a linear transformation.

Every introductory linear algebra course teaches methods for finding eigenvalues and associated eigenvectors of linear transformations T acting on R n and describes the geometric interpretation of such objects. My question pertains to the case of higher dimensional invariant subspaces - in particula...

- Mon Feb 04, 2013 9:52 pm UTC
- Forum: Mathematics
- Topic: Why do we need infinite sets again?
- Replies:
**20** - Views:
**2850**

### Re: Why do we need infinite sets again?

As far as I know, there's nothing wrong with taking the usual axioms of ZF but replacing the axiom of infinity with its negation. However you probably end up with something not very interesting and you certainly can't construct a set which we would ordinarily associate to the natural numbers or any ...

- Fri Feb 01, 2013 11:23 am UTC
- Forum: Mathematics
- Topic: Various Math Questions (previously "How a 'function' exists'
- Replies:
**40** - Views:
**8038**

### Re: Various Math Questions (previously "How a 'function' exi

You can't say that the series has a sum in the usual sense of the word sum. It is a divergent series and so it doesn't converge to any value in the usual definition of 'converge'. There are various ways that we can assign a value to the sum though, and it depends on what you want to do with a series...

- Thu Jan 31, 2013 2:32 pm UTC
- Forum: Mathematics
- Topic: An Infinite Length String and what it contains
- Replies:
**83** - Views:
**14395**

### Re: An Infinite Length String and what it contains

I suppose the setup would be that a machine picks an integer 0-9 uniformly randomly once every second and prints the chosen digit. This process continues indefinitely. What is the probability that at some point the finite sequence of digits (a

_{0}...a_{n}) is printed consequtively?- Sat Jan 19, 2013 2:55 pm UTC
- Forum: Mathematics
- Topic: Looking for a set of math problems from Discover magazine
- Replies:
**16** - Views:
**2427**

### Re: Looking for a set of math problems from Discover magazin

^ That's definitely the intended answer, but it has always annoyed me. Because: It's perfectly possible to have two children who are both 6, where one is the oldest. In some sense, it's impossible not to. I think it's a rather reasonable assumption that there is no oldest sibling in a p...

- Sat Jan 05, 2013 12:10 am UTC
- Forum: Mathematics
- Topic: C^k maps
- Replies:
**6** - Views:
**1169**

### Re: C^k maps

Your condition for Det(Jf) to be non-zero everywhere is probably enough for C

^{1}functions, but I'm not sure if it's enough for C^{k}, k>1 functions. It feels like you need to have some condition on the higher partial derivative as well as the first. It does seem like a reasonable conjecture though.- Thu Dec 27, 2012 4:02 am UTC
- Forum: Mathematics
- Topic: Dense geodesics on hyperbolic surfaces
- Replies:
**7** - Views:
**2178**

### Re: Dense geodesics on hyperbolic surfaces

This particular example should hopefully illustrate why we're really interested in l having the property that when we consider its image after quotienting out by Z^2, we want it to be dense in the torus. I find it easier to visualise if, instead of defining an acceptance domain and projecting accept...

- Thu Dec 27, 2012 4:02 am UTC
- Forum: Mathematics
- Topic: Dense geodesics on hyperbolic surfaces
- Replies:
**7** - Views:
**2178**

### Re: Dense geodesics on hyperbolic surfaces

[I've had to break this post up as it exceeds the character limit I think] What a lovely example! I understood what you've written fairly well and it seems like a very elegant way of studying these systems. I won't pretend that I see it as trivial though so I'll have to think about this a lot more b...

- Mon Dec 24, 2012 12:21 pm UTC
- Forum: Mathematics
- Topic: Proof of infinite ascent and finite descent for x^2+y^-z^2
- Replies:
**2** - Views:
**1841**

### Re: Proof of infinite ascent and finite descent for x^2+y^-z

press the edit button then

- Wed Dec 19, 2012 7:20 pm UTC
- Forum: Mathematics
- Topic: Fermat's Last Theorem
- Replies:
**76** - Views:
**13146**

### Re: Fermat's Last Theorem

I would just like to comment on lemma 3. Firstly, this is a well known result and almost trivial using the fundamental theorem of arithmetic. However, your proof is just plain incorrect. You can't start the proof by assuming that C=s m for some integers s and m. It happens to be true in this case bu...

- Thu Dec 13, 2012 2:59 pm UTC
- Forum: Mathematics
- Topic: Boy Girl Problem
- Replies:
**25** - Views:
**3370**

### Re: Boy Girl Problem

There's a whole series of articles at this site which are interesting (especially if you're a fan of Martin Gardner). I particular enjoyed reading the 'bracing polygons' article.

- Thu Dec 13, 2012 1:57 pm UTC
- Forum: Mathematics
- Topic: Boy Girl Problem
- Replies:
**25** - Views:
**3370**

### Re: Boy Girl Problem

This migth help http://arxiv.org/pdf/1102.0173.pdf .

- Wed Dec 12, 2012 12:06 am UTC
- Forum: Mathematics
- Topic: Integral of 1/x as a limit
- Replies:
**44** - Views:
**6359**

### Re: Integral of 1/x as a limit

That statement seems reasonable to me, but it's not being used to evaluate the limit. It's being claimed that C+lim y->p h(x,y) = lim y->p (f(x,y)+g(y)) = C'+lim y->p f(x,y) for some constant C'. The first equality is fine and is the final part of your statement. The second equality is not fine. g(y...

- Tue Dec 11, 2012 10:23 pm UTC
- Forum: Mathematics
- Topic: Integral of 1/x as a limit
- Replies:
**44** - Views:
**6359**

### Re: Integral of 1/x as a limit

The point is that you offered no justification, it's almost like you think that for all functions f, g, lim

_{y->p}(f(x,y)+g(y))=lim_{y->p}(f(x,y)+C) for some constant C. This is only true in general if g is continuous at p, and is certainly not true if g isn't defined at p.- Tue Dec 11, 2012 9:41 pm UTC
- Forum: Mathematics
- Topic: Integral of 1/x as a limit
- Replies:
**44** - Views:
**6359**

### Re: Integral of 1/x as a limit

Where did derivatives come in to this? the limit is with respect to n so you can't just 'merge' an n in to a constant. I think maybe you're confused by the use of the letter n as it's usually used for constants or at least integers. Instead of n, use y. Would you say that lim y->-1 (x y +y+C 1 )=lim...

- Sun Dec 09, 2012 2:02 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3536**

### Re: Subgroups of an arbitrary group

6) Show that if the element a is in C, then the element a -1 is also in C. It means that: if multiplying an element a in the group G by every element x of the group G, and the result I obtain is the same even if I swap the position of the elements, then that element a of the group G, is also in C. ...

- Sun Dec 09, 2012 12:56 am UTC
- Forum: Mathematics
- Topic: Integral of 1/x as a limit
- Replies:
**44** - Views:
**6359**

### Re: Integral of 1/x as a limit

How can it be equal to log(x)? Are you instead trying to show that lim y->0 [((x^y)/y)-ln(x)] = a in the supremum metric* of C(R + ,R) for some constant function a? If that's the case, it really should be stated. It doesn't matter if you try to use the supremum norm or not; it doesn't converge poin...

- Sun Dec 09, 2012 12:33 am UTC
- Forum: Mathematics
- Topic: Integral of 1/x as a limit
- Replies:
**44** - Views:
**6359**

### Re: Integral of 1/x as a limit

Am I missing something? For all x in the positive real numbers, lim y->0 (x y )/y doesn't exist. How can it be equal to log(x)? Are you instead trying to show that lim y->0 [((x^y)/y)-ln(x)] = a in the supremum metric* of C(R + ,R) for some constant function a? If that's the case, it really should b...

- Fri Dec 07, 2012 3:03 pm UTC
- Forum: Mathematics
- Topic: bijection from the set of all maps from N to N to R
- Replies:
**9** - Views:
**1690**

### Re: bijection from the set of all maps from N to N to R

I quite like the approach of coding them as binary numbers where f(i)+1 tells you how many 0s to put in a row and then f(i+1)+1 tells you how many 1s. So if f(n)=n, then g(f)=0.0110001111000001111110000000.... and if f(n)=1 for all n, then g(f)=0.00110011001100110011001100110011........

- Fri Dec 07, 2012 11:33 am UTC
- Forum: Mathematics
- Topic: bijection from the set of all maps from N to N to R
- Replies:
**9** - Views:
**1690**

### Re: bijection from the set of all maps from N to N to R

In case it wasn't clear to Afif_D, I should have probably explicitly said that I was making use of the Cantor-Bernstein-Schroeder Theorem.

- Thu Dec 06, 2012 8:38 pm UTC
- Forum: Mathematics
- Topic: Dense geodesics on hyperbolic surfaces
- Replies:
**7** - Views:
**2178**

### Re: Dense geodesics on hyperbolic surfaces

Thanks jestingrabbit. I think that's the sort of result that I need, although I have much more of a topological background so I'll have to spend some time understanding the dynamical result (although I'm slowly building up a discrete dynamics knowledge base at the moment). Would I be right in thinki...

- Thu Dec 06, 2012 6:00 pm UTC
- Forum: Mathematics
- Topic: bijection from the set of all maps from N to N to R
- Replies:
**9** - Views:
**1690**

### Re: bijection from the set of all maps from N to N to R

Recall that m^m=card(N N )=card( { f| f: N -> N }) so you want to find a function g: N N -> (0,1) which is surjective. Given some function f: N -> N, can you think of a natural way to assign some decimal number to that function? Given this function, can you find an injective function h: (0,1) -> N N...

- Thu Dec 06, 2012 1:31 pm UTC
- Forum: Mathematics
- Topic: Dense geodesics on hyperbolic surfaces
- Replies:
**7** - Views:
**2178**

### Dense geodesics on hyperbolic surfaces

This a rather vague question but hopefully someone can point me to some reading material which can help me find what I need. First a little context. Given some geodesic l in the plane R 2 , we have the following theorem. Let L be the image of l in the quotient space T=R 2 /Z 2 , the torus (Z 2 is th...

- Thu Nov 29, 2012 12:14 am UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3536**

### Re: Subgroups of an arbitrary group

That was a model answer and very well written. You'll find that a similar line of attack works pretty well whenever you're trying to show that some set with a certain definition is a subgroup of some superset which happens to be a group.

- Wed Nov 21, 2012 1:50 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3536**

### Re: Subgroups of an arbitrary group

You seem unsure of exactly what you need to show. Maybe it would help if I broke the exercise up in to smaller pieces for you. Let G be a group. Let H and K be subgroups of G. 1) What is the definition of H and K being subgroups of G? 2) What is the definition of H∩K? 3) What is the definition of a ...

- Thu Nov 15, 2012 12:07 pm UTC
- Forum: Mathematics
- Topic: Direct product of Groups
- Replies:
**10** - Views:
**3575**

### Re: Direct product of Groups

So for this part: Z 2 xZ 3 = {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2)} (0,1)+(0,2) = (0+0, 1+2) = (0,3) (0,1)+(1,2) = (0+1, 1+2) = (1,3) (0,2)+(0,1) = (0+0, 2+1) = (0,3) (0,2)+(0,2) = (0+0, 2+2) = (0,4) (0,2)+(1,1) = (0+1, 2+1) = (1,3) (0,2)+(1,2) = (0+1, 2+2) = (1,4) (1,1)+(0,2) = (1+0, 1+2) = (1...

- Tue Nov 13, 2012 10:55 pm UTC
- Forum: Mathematics
- Topic: Limit of a Changing Probability Distribution
- Replies:
**22** - Views:
**4584**

### Re: Limit of a Changing Probability Distribution

There's the possibility of both case 1 and 2 occurring in an infinite sequence of events E j so I suppose what you really want to know is what is the probability of each case occurring. I'd assume that case 1 has probability 1 of occurring and case 2 has probability 0 occurring but I'm not well-vers...

- Tue Nov 13, 2012 7:46 pm UTC
- Forum: Mathematics
- Topic: Analogue of isomorphism theorem for orbit spaces
- Replies:
**0** - Views:
**1717**

### Analogue of isomorphism theorem for orbit spaces

In case anyone is wondering, this isn't homework - just a thought I had that I'd like to resolve. Recall the third isomorphism theorem for groups which says that if G is a group, N, K are normal subgroups of G and K is a subgroup of N, then we have: The quotient N/K is a normal subgroup of the quoti...