Lecture 18(Wedneday) - CSC 165 epsilon/delta Danny Heap...

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Unformatted text preview: CSC 165 epsilon/delta Danny Heap heap@cs.toronto.edu http://www.cdf.toronto.edu/ f heap/165/F10/ slide 1 a continuous example The claim below says that the function x2 is continuous at . In proving the claim you can't control the value of " or x, but you can craft to make things work out. For every positive real number ", there is a positive real number , so that for every real number x, if jx j < , then jx2 2j < The claim is true. The proof format should be already familiar to you. A good approach is to ll in as much as possible, leaving the actual value of out until you have more intuition about it. 25 x*x pi*pi 20 15 10 5 0 0 1 2 3 4 5 slide 2 scratch slide 3 using uniqueness Suppose you have a predicate of the natural numbers: Is S (3 3) true? How do you prove that? It's useful to check out the remainder theorem from the sheet of mathematical prerequisites. Vn P N S (n) D Wk P N; n = 7k + 3 slide 4 ...
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This note was uploaded on 10/13/2011 for the course COMPUTER S CSC 165 taught by Professor Dannyheap during the Fall '10 term at University of Toronto- Toronto.

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Lecture 18(Wedneday) - CSC 165 epsilon/delta Danny Heap...

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