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Indeed, if a number x satisfies a +x = a for any one number a, then x = 0 (and consequently this equation also holds for all numbers a). In passing we might ask just when a — b does equal b — a, and it is amusing to discover how powerless we are if we rely only on properties P1-P4 to justify our manipulations. Bought this particular textbook because of its connection with the Hampshire College Summer Studies in Mathematics program, if I remember (the index of this, or another, of Spivak's books has an in-joke listing for "Yellow Pigs", not a would-be counterculture insult but rather one of the two mascots of that program, along with the number 17.

Like putting an everyday object under a microscope: very interesting, but now there are many more interesting objects I want to put under a microscope. This is a beautiful exposition of the theory of calculus from the axiomatic approach with full motivation and proof of the major theorems and some interesting facts that are seldom presented at this level.As other posters have said, if you are going to be a mathematics or physics major, there is no reason to even look at another calculus text. Moreover, the Appendix to Chapter 12 has been extended to treat vector operations on vector-valued curves.

The assertion that 1In the preface to the third edition I noted that it was 13 years between the first and second editions, and then another 14 years before the third, expressing the hope that the next edition would appear sooner.

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