Proving God Existence

[Zarith]

Set 1: All Statuses separated from (1/1/2000 00:00:00) by a finite number of seconds
Set 2: All Statuses separated from (1/1/2000 00:00:00) by an infinite number of seconds
S1= {U(1), U(2), ….}, S2={U(-∞), U(-∞+1), U(-∞+2),….}

2. S1 has infinite no. of elements
False, as it contradicts with the definition of Set 1; it has only Statuses separated by a finite number of seconds so it must have a finite No. of elements.

I read through some of this, but there's 34 pages here, so sorry if this has already been cleared up.

The definition of S1 is to me ambiguous. Either you are saying that:
1) S1 contains all states which are separated in time from 1/1/2000 00:00:00 by an amount that is smaller than some arbitrarily chosen fixed constant number T1, or ...
2) S1 contains all states which are separated in time from 1/1/2000 00:00:00 by some finite number, this number being different for different members of S1

If you mean definition (1), then S1 contains a finite number of elements and S2 contains an infinite number of elements.
If you mean definition (2), then S1 contains an infinite number of elements and S2 is empty.

To see why (2) entails an infinite S1, note that given any member of S1 at time T0, a new member of S1 can be generated at T1=T0+1. T0 is finite therefore T1 is too.

This should have been obvious, since you can't start with a set containing an infinite number of elements (the integers), split it, and end up with a finite number of elements in the union of the 2 resulting sets.

I stopped reading after this.