Learning Spivak's Calculus Edition 3 - Different Approaches?

[tehdiddulator]

I recently obtained a copy of Spivak' Calculus edition 3 and started going through the book. I've found that there is more than one way to prove what he is asking in his problem set and I'm wondering if this is a problem as to how he is trying to teach the subject? I would think not, but I'd like to learn his textbook how he wants it to be taught.

 

[BloodyFrozen]

Sometimes, the way he wants you to do it is built upon in later chapters. Also, in the beginning of the book, many of the Properties of Numbers problems seem trivial, but he wants you to do it a certain way (possibly) using certain properties and justifying him. However, finding other ways to prove results is also very good and beneficial.

 

[slider142]

It will always build mathematical maturity to prove a result in more than one way. However, it is important to be sure that your proof is not a tautology, in that the theorems you use are implied by what you are trying to prove. Ie., in the first chapter, you should not use the binomial theorem or synthetic division, unless you can prove these theorems yourself, before they are presented in the course of the text.
In essence, he expects that you can use only the material presented in the previous chapters and exercises to work on the current exercise.