Recent content by Tzar

In general there are infinitely many groups that can go in the middle of a short exact sequence. In fact they are in one to one correspondence with elements of Ext^1(Z_4,Z) (which is an Abelian group). Now if this Ext group is zero, then you know for sure, the middle term must be ZxZ/4...

Why is an isomorphism any more intuitive then a homomorphism?? An isomorphism is just a homomorphism which has an inverse which is also a homomorphism. In fact categorically, that's how an isomorphism is defined, so you can't even define an isomorphism until you have the notion of a...

I've always struggled to understand that statement made by Godel. It makes sense (to me) that you can always ask a question which can not be proved nor disproved by your axioms. However, how can you claim a statement is true, if it is not provable in your theory?

I agree it is a very interesting question but depends on what we mean by "direct" proof. What makes a proof direct or indirect? Certainly in mathematics one can prove the existence of certain objects and constructions without actually constructing them. In certain proofs, a heavy reliance on...

oh ok sorry

tgt, I think you are missing the point. When you use the word "group" that means that you already know how to multiple elements together, its part of the data for that group. The actual labels that are assigned to the elements is irrelevant: you can all the elements a, b, c or 1,2,3 or whatever...

The difference is quite significant. An R-module M is firstly an abelian group; it has not multiplicative structure. An R-algebra A is a ring which when you forget about the multiplicative structure is also an R-module. To show you an example of a module that is not an alegebra: pick your...

You probably mean at least 40% then :) I think I heard of that result as well. I would assume that the proof would need to be heavily combinatorial, but if someone knows more, please tell us! CRGreathouse you might also find the following results interesting...

We know that the non trivial zeros must have 0<Re(s)<1 but that's about it. We have many examples of zeros with Re(s)=1/2 and in fact is has been proven that there infinitely many zeros with that property. However we still haven't proved that you can't have a zero with 0<Re(s)<1 but Re(s) not...

Thank you ver much for your help..However, for some reason when I try to use the rotating package, it simply doesn't work. I type the command to rotate (after loading the package) and it simply doesn't rotate, it just prints the symbol (or any other text when I try) normally. I don't get an...

How do I do that?? Is there a specific functon that allow me to rotate any given symbol??

no no. what I am trying to achieve is like a commutative diagram but with with "subset" symbols instead of arrros. So for example, one of the ros may be A\subseteq B. I need the analogue of this but for columns. The \cup and \cap sublos won't do, for they don't have a slash next to them...

Does anyone know the symbol for a vertical subset symbol?? i.e the equivalent of \subseteq but which points up (i also need one which points down)?? Thank for the help

The main problem of tyring to solve sudoku through matrices is the fact that the solution needs only to contain numbers 1 through to 9. This restriction can't be expressed in matrix form, I think... OR can anyone think of a way of doing that?

The question you ask is a good one. I have spent quite a bit of time thinking about it, and well got almost nowhere. I believe that the fact that white goes first does give white some advantage. Statistically speaking I think white wins slightly more often. So I believe that if white plays...