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I probably muddied the water using Hilbert's hotel as an analogy in a way other than what the paradox was originally used.

In Hilbert's paradox the statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.

My point is more like, what happens to the person in the end room?

Our inability to observe or conceive such large time frames doesn't prevent us from conceiving this time frame plus one. Therefore the time frame can't exist as an actual infinity.

HoloKat 2y ago

That doesn’t make sense. There’s nothing to state that a time frame plus one is proof of no infinity. Plus one just continues the infinity.

The general consensus is that we lack knowledge about what happens to the universe after it cools. It’s all speculation without any proof whatsoever.

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Azz 2y ago

I think we are talking about different things.

There is a difference between potential infinity, which refers to a procedure that gets closer and closer to, but never quite reaches, an infinite end, and an actual infinity, or completed infinity. An infinity that one actually reaches; the process is already done.

Dealing with a mathematical concept of a complete infinity, such as complete sets of natural or real numbers is different to the question of whether infinite things exist physically in nature.