Autodidact pointed out that it was nonsense to talk about non-existence coming into being.
She actually said "Hello, it doesn't exist!".
You then said that if "non-existence" never was, then "existence" is both eternal and infinite.
Okay. Now that we recall correctly, let's look at this. Autodidact meant that non-existence, by definition, does not come into being. That does not mean that non-existence is impossible and it certainly does not mean that existence is both eternal and infinite.
OK, if you claim that non-existence is possible, then it follows you are now contradicting Autodidact who concluded that it doesn't exist. And so my next question to you is, if you believe non-existence is possible, how does it..ahem..come to be?
My argument is not with your assertion that "existence" is eternal; I think the argument can be convincingly made that "existence" is without beginning or end -- not that that argument amounts to much. My problem is with this harebrained way of ignoring context and meaning to leap to unwarranted conclusions. It makes it very difficult to try to communicate with you.
So if existence is eternal as you believe it to be, do you not see that it logically follows that non-existence, which you believe is not an impossibillity, can not...ahem...come into being, for if it were to, then existence can't be eternal.
Personally my understanding also is that existence is eternal and hence my interest in trying to understand how Big Bang theory is framed in the context of cosmological conceptual framework of eternity and infinity. So if you would like to be constructive in this undertaking, try to factor this into your answers to my questions.
Thank you in advance for helping to clear up any confusion.