/jp/ - Otaku Culture

[Anonymous No.]

Suppose that we have a set of five cats. We wish to prove that they are all the same color.

Suppose that we had a proof that all sets of four cats were the same color. If that were true, we could prove that all five cats are the same color by removing a cat to leave a group of four cats.

Do this in two ways, and we have two different groups of four cats. By our supposed existing proof, since these are groups of four, all cats in them must be the same color. For example, the first, second, third and fourth cats constitute a group of four, and thus must all be the same color; and the second, third, fourth and fifth cats also constitute a group of four and thus must also all be the same color. For this to occur, all five cats in the group of five must be the same color.

But how are we to get a proof that all sets of four cats are the same color?

We apply the same logic again. By the same process, a group of four cats could be broken down into groups of three, and then a group of three cats could be broken down into groups of two, and so on. Eventually we will reach a group size of one, and it is obvious that all cats in a group of one cat must be the same color.

If you expand by induction, this shows all groups of n cats are the same colour. therefore all cats in the world are the same colour.