Recent content by Buri

Hi I've looked up the definition of an ordered field and I've found two slightly different ones. One is that an ordered field is a field with a total order, but I've found another which requires it to also satisfy: (1) If a <= b then a + c <= b + c (2) If 0 <= a and 0 <= b, then 0 <= ab...

Sorry for all the typos I'm on my phone lol

I'd like to make sure of something. To begin with d/dx will denote partials. My text (Complex Analysis by Steine and Shakarchi) derives the equality df/dx = (1/i) df/dy. To derive this it considers the difference quotient by letting h be real and purely imaginary in another case. But it let's...

I'm a 3rd year mathematics specialist student at the University of Toronto. I'll be taking four graduate courses next year (DG II, ANT, CA II, CT) and all the others are 300 level. Here it goes: Fall Groups, Rings and Fields Complex Analysis I Topology Differential Geometry II Algebraic...

I've read your lasts post and thanks a lot. I get it now. Thanks for your help :)

I have to head out right now, but I'll read your further posts later today. Thanks.

I see how this works now. I'll work out a longer one just to do it myself. Thanks a lot for you help. I feel like I understand this stuff a lot better now :) I appreciate your help :) Thanks :)

Ahhhh this is starting to make more sense to me now :) So I guess that's what I was doing wrong before and it only worked until I actually wrote these functions out like you just did. So I guess I should really just think of these as functions and ignore the entire position thing because its...

I see. So how would I then be able to write {k,2,3,...,k-1,1} as a composite of elementary permutations? It just seems that I'll have to swap two non-consecutive numbers to do so. And just a question about compositions. if I have to permutations f and g. g will permute {1,2,...,k} some set...

But I guess if it means position and value, in my case since its the set I = (1,2,3, ..., k) that I'm permuting the position and the value are the exact same thing.

So the i and i+1 aren't the values of the permutation? But rather the position (that is adjacent values)? See like {1,2,3,5,6,7}. Would an elementary permutation be able to swap the 3 and 5? Because I'm confused as to what exactly is meant by the e_i (i + 1) = i and e_i (i) = i + 1...

So the i's in the above refers to the position of the numbers? Or does that literally mean f(i) = i + 1 so for example f(2) = 2 + 1 = 3. Or does that refer to, a is in position 2 and b is position 3 so therefore, f(a) = b and f(b) = a.

I don't know transpositions...see all I know about permutations is basically what's on the page I posted. Its not a course in group theory, but analysis and the permutations are only being introduced to develop the alternating tensor.

Okay, I understand that in sets order doesn't matter but since they're permutations and frankly the notation {1,2,...,k} is wrong, but with the order the permutation premutes the elements of the set (assuming some initial order). But then another permutation is always acting on this set to...

I'm not exactly sure what you're saying. So does it mean that they act on a set that has some order defined on it? Like if I'm looking at S_k and looking at the permutations of {1,2,...,k} the permutations always act on this set in this exact order. So it wouldn't make sense for me to apply a...