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I am a mathematician I don't need examples. What is your formal definition of a mapping. In mathematic it is normally used as a synonym for a morphism in a given category and in th…

Look up Peano arithmetic to see how one proves 1+1 = 2 within the standard formal system.

A function is a relation for elements in a to elements in b such that for every element in a there is a unique element in b. This is vacuously true of the empty relation when a is …

There is a very natural definition of numbers as sets. We define 0 to be the empty set and we define the successor function by S(x) = {x} union x. Then the natural numbers are the …

This is not true. A very natural way to define a^b is as the number of functions for a set with "b" elements to a set with "a" elements. In this case there is exactly one function …