Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I: | (16) |
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All of Spivak Chapters 2 and 3.
From Spivak Chapter 2: 1, 5.
From Spivak Chapter 3: 6, 13.
From Spivak Chapter 2: 3, 4, 12, 22.
From Spivak Chapter 3: 1, 7, 21.
An extra problem: Is there a problem with the following inductive proof that all horses are of the same color?
We assert that in all sets with precisely horses, all horses are of the same color. For , this is obvious: it is clear that in a set with just one horse, all horses are of the same color. Now assume our assertion is true for all sets with horses, and let us be given a set with horses in it. By the inductive assumption, the first of those are of the same color and also the last of those. Hence they are all of the same color as illustrated below:
From Spivak Chapter 2: 27, 28.
A little more on Chapter 2, Problem 22:
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