Proof Example

Greetings I am back!  Finally a week without a midterm!  I only have the assignment for this course and a linear algebra problem set to do this week, this is practically a week off at U of T.  Do you want to know something scary?  One of my friends has yet to write any blog posts, and I am not even sure if he has set up blogger!  Yikes!  In this post I will be writing a nice proof of our quiz 5 question.  Last week I did not attend my usual tutorial time because of a time conflict so I got the chance to see another TA do proofs.  I can say that for the most part both TA's did proofs the same, but there were a few subtle differences.  Anyway, without further ado:

I answered this a bit differently on the quiz by leaving the j variable blank at first and then setting it after I had solved, but I think this way is cleaner and more logical.  I have noticed that I am pretty good at algebraic proofs like this one, but still have some trouble with epsilon delta style proofs.  Another proof is incoming this week! Until then!