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I understand that this should be done by induction, but I have very limited knowledge on proof by induction. Could someone explain it in a way which also makes clear exactly what each stage of induction means and achieves?

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    what is the def. of peano finite? I assume dedekind finite is what's said here https://en.wikipedia.org/wiki/Dedekind-infinite_set2012-11-17
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    A set is Peano finite if there is a bijection between the set and a natural number. It is Dedekind finite if it is not equivalent to a proper subset of itself (the same as is in the link).2012-11-17

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