What is eternity without time?

The RCI National Youth Rally ran over the Australia Day long weekend. Each attending young peoples group was asked to bring a short film. The Newcastle film showed our answers to a series of random questions. One of these questions was: What is eternity without time? The Bible (Gods Word) records a promise of eternal life. We are also told God operates outside of time. So, if we’re living with God, outside of time, for eternity… what is eternity?

Hopefully you can see what we were trying to ask.

Four weeks have passed, and until recently I was never really satisfied with my answer(s). The problem with previous answers, I think, is we never totally established that time would be abolished. However, for the purposes of answering the question, as it was presented, assume that time ceases to exist at some point (point? that requires a measurement: sigh) after the return of Christ.

Time is a unit of measure. The popular concept of eternity is existing for a limitless amount of time [Wikipedia]. Eternity is a quantity that we measure with time, that we will never finish measuring. I’m sorry, but now I have to use Math. We can create a bijective function, between the quantity of eternity, measured to a particular instant, and the set of natural numbers. Therefore the set of measurements of eternity is countably infinite. But it is countable.

You can always take the largest natural number you can imagine and add one, allowing you to take another measurement of eternity.

So without time, eternity either:

1. Finite, because we do not have a unit that is bijective to the set of natural numbers. Or;
2. Meaningless by definition.

Re-reading this post, I am suggesting that time would not cease to exist. That changes the fundamental point of the original question. Of course, this is applying human Math, it is probable that or understanding will change in time (excuse the pun). We may never get it right, we may only understand when we put on the mind of Christ.

What do you all think?