Recent content by mathemasochist

Oops, you're right. I looked back at the text, and Spivak includes the additional condition that A is a set of natural numbers. Then the problem becomes proving that A contains all the natural numbers. Does specifying this condition fix my proof?

I was trying to prove induction in general using the well-ordering principle. Here is the precise statement I was trying to prove: If A is a set such that 1 is an element of A and k+1 is in a whenever k is in A, then A is the set of natural numbers. I don't know what the precise definition of...

Homework Statement Prove induction from the well-ordering principle. Homework EquationsThe Attempt at a Solution So my attempt is similar to what Spivak uses to prove well-ordering from induction. Let A be the set equipped with the following properties: 1. 1 is in A 2. For every k in A, k+1...

Would you say that it's worth it to take notes if you can just find all the material in the book anyway?

Hi. Inexperienced self-studying student here. I know it's very commonly repeated that you can't force yourself to absorb some topic all at once, but I was wondering if you could feasibly get through a book on a topic like analysis with 2 months of time "on average." And by that, I mean something...