Re: Infinite sets.

Hi,

I have a question.
If we can define "infinite set" in the following manner.
X is infinite <-> Ax: x in X -> ES(x):S(x) in X.
were S(x) stands for the successor of x.

If I read this correctly, your definition of "infinite" will not
include the set of even numbers X = { 0, 2, 4, ... } since for no
element x in X is S(x) in X.

Likewise, by your definition, the empty set is infinite, since you
cannot find an x in X where S(x) is missing.

In the end, the question is simply this: why are you trying to create
new "definitions" for mathematical terms that are already appropriately
defined?

.

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