Logic1104 - Generalized induction n4 1. 2. 3. The least...

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HW #7 (due 11/11) 1. By using one of the induction prin- ciples, show that every natural number greater than 1 is a product of prime num- bers. 2. Show why Theorem 15.1 follows from Theorem 15.4 (this actually shows Theor- ems 15.1-4 are all equivalent to one an- other).
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Never miss a class unless you missed it last time Q. If you follow the above instruction, do you have to attend the first class? G For every class, either you missed the class last time, or you don’t miss the cur- rent class. But there was no class before, and you cannot have missed it. Therefore, you must attend the first class, and every class thereafter.
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15.6 (theorem 15.4, finite descent) (1) For any n, if P fails for n, then P fails for some natural number less than n. Then P holds for all natural numbers. (Proof) (1) ± For any n, if P holds for all numbers less than n, then P holds for n (complete induction). Why is it called “finite descent”?
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This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

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Logic1104 - Generalized induction n4 1. 2. 3. The least...

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