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BEGIN QUOTE

Definition. If there exists a 1-1 mapping of A onto B... we write A~B. ...This relation... is called an equivalence relation.

Definition. For any positive integer n, Let J_n be the set whose elements are the integers 1, 2, ..., n; let J be the set consisting of all positive integers. For any set A we say:

a) A is "finite" if A~J_n for some n (the empty set is also considered to be finite).

b) A is "infinite" if A is not finite.

END QUOTE

I just want to define infinite by writing out the negation of a).

I wasn't sure if I had to change "some n", so I tried to rewrite a) using what FOL I know, but couldn't figure out how to combine all the requirements of the equivalence relation. I end up with several sentences. Is there a simpler way?

Ugh,

Rachel

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# Proper Negation

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