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#1 2005-10-30 06:55:17

barrence
Guest

Mathematical Induction Conundrum

First Conundrum:

If possible, describe an induction principle for the set of
{0,−1,−2, . . .}. If this is not possible, give a brief explanation of why
it is not possible.

Second Conundrum:

Determine if there is a problem with the following proof by
induction that ‘all Canadians live inWaterloo.’ Give a brief explanation
of the problem.
Base case: consider the group of 0 Canadians; clearly all the Canadians
in the group live in Waterloo.


I.H. For any group of 0 <= k Canadians, all those k Canadians live in
Waterloo.
Consider a group of k + 1 Canadians. Remove Canadian c from the
group. The group consists of k Canadians, by the I.H. all those k
Canadians live in Waterloo. Pick one of the k Canadians, say d, d
lives in Waterloo. Remove d from the group and replace d with c. The
group still has k Canadians so, by the I.H., they all live in Waterloo.
Therefore all the k + 1 Canadians live in Waterloo.

#2 2005-10-31 19:28:30

barrence
Guest

Re: Mathematical Induction Conundrum

I'm not too sure I understand your notation for the solution to the first problem, could you restate that?

thanks for your patience

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