Recent content by Bruce Wayne1

Hello! One of the many aspects of math that I'm intrigued by is pedagogy. I find that many times folks grow up thinking certain mathematical statements that in the end may be inaccurate, or totally false. I came across a little pic on the internet, and it says "f(x) is just a fancy way of...

Yes, exactly. I want to show that a cyclic group G of order n is isomorphic to Zn. I understand the concepts, and I know how to prove it for a relatively small n, but I haven't been able to find a completed proof online. I'd like to read it, and ask a few questions on the theory of why it works...

Hi! I'm trying to prove a cyclic group is isomorphic to ring under addition. What the strategy I would take? How would I get it started? Here's what I know so far: I need to meet 3 conditions-- 1 to 1, onto, and the operation is preserved. I also know that isomorphic means that the group is...

Thanks! I have seen different proofs use "claim", and I do see that it makes a difference, though I didn't think of that here. Could you explain to me a bit better why claim is different than suppose in math proofs? Truth is, I did terrible in high school geometry, and the math courses I took...

Thanks! It was a lot simpler than I had anticipated. (Smile)

Hi! I'm trying to show that for each element x ∈ R, there is a unique element y ∈ R such that x + y = y + x = 0. (denote y by −x.)

I'm working on showing that Z3 is a ring. The one portion I'd like to confirm is the additive inverse part. So here's what I'm thinking as my proof: Given [x]3 , suppose [3-x]3 is the additive inverse in the set Z3 . Thus: [3-x]3 = [3]3 + [-x]3 = [0]3 + [-x]3 = [0-x]3 = [-x]3 Then, it...

Thanks. Here's my attempt: Assume the linear transformation $\mathbf x \mapsto A \mathbf x$ maps $\mathbb R^n$ onto $\mathbb R^n$. For all $\mathbf v \in \mathbb R^n$ there is at least one vector $\mathbf x \in \mathbb R^n$ such that $A \mathbf x = \mathbf v$. $A \mathbf x = \mathbf v$ can be...

Correct, I am trying to prove ( h)<-->(i) from that list. I'm trying to do it directly between those two, without using the others. However, I do understand (g) can be used, as I tried, but how do I justify it? In other words, I need to have it justified. I'm not looking to just say "oh...

I've been watching the OCW Linear Algebra course and I have a textbook, and I came across something that I think is fascinating: The Invertible Matrix Theorem. I've seen some proofs and I find that a lot of the statements are linked in different orders and sometimes the author will site one tiny...

Sesame Street's resident mathematician: Count von Count. Ok ok ... I have to be honest and say I'm not sure I can pick a favorite, simply because math has had so many wonderful contributions over the centuries. I do, however, favor the mathematicians that spoke French (not necessarily themselves...