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function increments its argument if it is a natural number and leaves it as is otherwise; the number 0 does not appear in the range of .As is the set of the elements of not in go on with

This is the set image of a set under , sometimes denoted by as well. Applying function to a set x simply increments every natural number in it. In particular, never contains the number 0, so that for any sets x and y,

Further, define

By

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