- #1
PFuser1232
- 479
- 20
So recently, I started reading Michael Spivak's "Calculus" to shore up my understanding of the subject, after being told that this text is well-known for its rigor. In chapter one, he lists 12 properties (or axioms) of numbers (distributive law, trichotomy law, and closure under addition, to name a few). I have a problem with the exercises for that chapter. They seem extremely trivial at first sight (for example, prove that ##\frac{a}{b} = \frac{ac}{bc}## for ##b, c ≠ 0##), and that's the problem. I can't understand the approach that is expected to be followed while answering such questions. Should I put myself in the mindset of someone who has never learned algebra before, and solve these questions (however redundant they may seem) in a systematic way that employs the 12 properties listed earlier in that chapter? Or should I proceed with whatever procedure I had been using before starting the text?