There wasn’t a single problem in particular I found took me a long time. It was more… when I finished a set of exercises, I looked at the clock and realized a couple of hours have gone by, and that seemed way too long (though it really wasn’t).
For example, the first chapter deals with properties of numbers (multiplicative/additive inverses and identities, associative laws, etc.) and using these properties in proofs. Some of the exercises, say, #4, are split up into several other exercises (i, ii, iii, iv, etc.). “Prove: if a > 1, then a^2 > a”—Which seemed fairly trivial to me at first, but proving them using only the properties of numbers/inequalities provided made the task more difficult.
During the time it took for me to solve them, I just… well… sat down and solved them. Played around with what I could and couldn’t do, referred to some proofs he mentioned earlier, etc. :)
There wasn’t a single problem in particular I found took me a long time. It was more… when I finished a set of exercises, I looked at the clock and realized a couple of hours have gone by, and that seemed way too long (though it really wasn’t).
For example, the first chapter deals with properties of numbers (multiplicative/additive inverses and identities, associative laws, etc.) and using these properties in proofs. Some of the exercises, say, #4, are split up into several other exercises (i, ii, iii, iv, etc.). “Prove: if a > 1, then a^2 > a”—Which seemed fairly trivial to me at first, but proving them using only the properties of numbers/inequalities provided made the task more difficult.
During the time it took for me to solve them, I just… well… sat down and solved them. Played around with what I could and couldn’t do, referred to some proofs he mentioned earlier, etc. :)
That sounds normal. Spivak isn’t an easy book, from what I’ve been told.