Quora: Ending without Beginning?

Can mathematics proof an ending can exist without a beginning? Can the universe itself have no beginning but has an ending, and at the ending it can't go back to the beginning?

"It depends on how you define beginning or ending. If a set has no beginning, the only way to define it is by the end: since you then start defining the set from the end, it would actually be the beginning. (E.g. you can define the set of all negative numbers as any number below 0, so you "start" writing the set down with -1 even though that's actually where the negative numbers end.) There's no formal definition for what "ending" or "beginning" means in mathematics, so, informally, it's just where you start and end a set. You can "prove" that you can begin a set without ending it by defining it that way: for example, natural numbers have a beginning but no end.

However, because there are infinitely many natural numbers, a random natural number would have to be selected from among infinitely many numbers, so that that random number would itself be infinite: therefore, there would be infinitely many smaller (and larger) natural numbers than the random number. If the present is  a random moment in an infinite set of moments, then the past and future would both be infinite."