Deseret Evening News, 9 February 189 ?

I’d love to look up the original text.

Option 1
Heavenly Father offers unity at some t1 = -∞. The Son and Holy Ghost accept at some time t2 = -∞.

I objected to this scenario saying it doesn’t make any sense – that it isn’t mathematically sound. Everybody agrees. /yay

Option 2
Heavenly Father offers unity at some finite time t1, and acceptance similarly comes at some time t2.

If this is the case, then there will be a point in the past where the Godhead did not exist.

Option 3
Heavenly father offers unity repeatedly in some denumerable way creating a whole set of times T1 = {t1,t2,t3,…}. The offer is accepted in some denumerable way creating a whole set of times T2 = {ta,tb,tc,…}. Both sets, T1 and T2 have the same cardinality (aleph0).

Conclusion, mathematically sound (given time is not a continuum).

So, hopefully my initial confusion (my apologies) has been cleared up and everybody is on the same page now.

Now, it shouldn’t be taken that my agreement with the math of your posited setup means agreement with the theology. One could equally posit that the Father offers unity every billion years {t1,t1+1E9,t1+2E9,…} and that the Son and Holy Ghost only accept every six billion years {t1,t1+6E9,t1+12E9,…} and still both sets will have the same infinite size. And by the same reasoning one is allowed to say in the above scenario “that there is no time at which the Godhead does not exist and that the Godhead exists at all times of an infinite array of times.”

Disclaimer: Of course, this scenario is only valid if we allow time to be a discrete sequence of events (which I personally tend to believe). If we instead think of time as a continuum then the argument has to be adjusted.

Clark is correct. There simply is not a point that is an infinite distance from now. Once again, infinity is a property of the entire set of points and not of any given point. Any given point does not have the property of being infinitely distant from anything any more than the number 4 has the property of being an infinite number though it is a part of an infinite set of numbers. You continue to commit the fallacy of division regarding infinite sets.

I think I miss your point as well.

PS: These are the definitions I’m working with:

Set A is a proper subset of set B iff all the members of A are also members of B, but not all the members of B are members of A.

The cardinality of a set is the number of members it contains.