(February 13, 2018 at 8:05 pm)Grandizer Wrote:(February 13, 2018 at 7:58 pm)RoadRunner79 Wrote: Can you add one more? How about subtract one more? If so, then how is it complete?
Edit: Or what do you mean by complete?
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.
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If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther