Jesus as Lord - why is this appealing to so many?

[GrandizerII]

Forget the hotel example.

Let's do set theory. Complete as in every possible element of an infinite set of integers (infinite both ways) is already there. How can you add more new elements to the set when it's complete?

You can simultaneously add +1 to each of the elements, sure, and each of the elements will then increase by 1, but it would still be the same infinite size because it's complete (I think, correct me if wrong, guys).

You ask, how can more numbers be added if it is complete, but by definition an infinite amount is never completed.    I think you are switching to sets now, because you can abstractly complete the set just add "..." .  You loosely define it, to include any possible integer.   You want to increase the set... you just loosen the definition.  So you either end up with a contradiction (it is both complete and not complete at the same time in the same way).   Or what you mean by complete is not the same.  Or you mean infinite in another way.

I switched to sets for your sake, not mine. We can go back to Hilbert's Hotel if that's what you really want. Hilbert's Hotel is completely occupied in terms of all rooms representing each integer from 0 to positive infinity. So represented by the infinite set of all whole numbers. But we can also change the example so that the hotel is infinite both ways, and there are rooms representing negative integers. Doesn't matter.

Complete, in the context of infinity, means every element of the concerned infinite set or sequence or whatever you want to call it, is there. And yes, in mathematics, infinite sets like infinite sets of integers are complete already. But what I cannot do is then represent that literally in writing because then it would be me trying to complete a potential infinity (assuming classical concepts of motion and time). What I write or draw is different from what is in the abstract math world.

But even going back to Existence itself, there is nothing logically impossible about actual infinities existing. So long as they are already complete, I need NOT complete anything. And so logically, it can exist in the real world. That's the logic. What you seem to have a problem with is how can a complete actual infinity be a thing? But this is more a problem with your intuition rather than with logic (so incredulity is not enough, you need to demonstrate on paper that it is a logical problem).

No one can perhaps really fully grasp infinity intuitively, but part of what's amazing about it is that it's counterintuitive. There are no contradictions happening with infinity, only apparent paradoxes. This is expected when we're dealing with infinity.