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# Can you find the fallacy in this inductive argument that all things are the same?

Asked by LostInParadise (22902)
August 29th, 2014

In honor of the start of the school year, here is what I think is a fairly interesting use, or rather misuse, of mathematical induction. When I first saw this problem, it took me a while to catch the flaw.

To prove: Everything is the same as everything else.

Base case: n =1. Obviously everything is the same as itself.

Inductive step: Assume that any n things are the same as each other. Choose any group of n+1 objects. The first n are all the same by the inductive assumption. So are the last n. Since the two groups overlap, all n+1 objects must be the same.

We conclude that any number of objects are all the same, that is, everything is the same as everything else.

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