Abstract
A natural number n always has a unique predecessor; it is either n - 1 or 0. The word “predecessor” will be understood to mean “immediate predecessor”. This is the fundamental concept in the theory of the natural numbers. If one takes “successor” as the basic concept and then postulates the existence of a sucessor to every natural number, one requires there to be an infinitely many numbers; the existence of such an infinite collection is not at all easy to prove.
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