Main post link -> http://blog.brilliant.org/2013/02/21/you-are-inductively-calvin/
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Are you convinced that induction has proven your name to be Calvin?
Just how powerful is Induction? I'd use it to show that your name is Calvin.
Claim: In a group of \( n \) people, everyone has the same name.
Proof: Let's show that condition (1) holds. In a group of \( n=1 \) people, all of them have the same name.
Let's show that condition (2) holds. Since the positive integer \( k \) is in the set, this means that in a group of any \( k \) people, all of them have the same name. So let's consider a group of \( k+1\) people. Since the first \( k \) people have the same name, and the last \(k \) people also have the same name, it means that all \(k+1\) of them must have the same name.
Thus, by Mathematical Induction, the set \( S \) includes all positive integers, so in a group of \(n \) people, everyone has the same name.
In particular, since my name is Calvin, and you are in the set of all \(N \) people on Earth, it follows that your name is also Calvin.
The above is adapted from Polya's proof that "No horse is of a different color".