Braininvat » September 3rd, 2018, 6:35 pm wrote:Seems a bit like saying there can't be any odd numbers because of the even numbers crowding them out in their infinitude. Brent, an infinite space is a continuum and has abundant room for infinite sets of anything - atoms, beach balls, short bald men named Balthazar, you name it. Have you read the thread here prior to posting? If nothing else, look up Hilbert's Hotel, and see how there's always room for more guests.

in·fi·nite

ˈinfənət/Submit

adjective

adjective: infinite

1. limitless or endless in space, extent, or size; impossible to measure or calculate.

"the infinite mercy of God"

synonyms:boundless, unbounded, unlimited, limitless, never-ending, interminable;

MATHEMATICS

greater than any assignable quantity or countable number.

MATHEMATICS

(of a series) able to be continued indefinitely.

You will notice that in Mathematics, they use potential "infinities" within a relative context.

For an actual Infinity, you need not other word but "boundless". For anything to be truly boundless, then nothing can exist beyond it. In an absolute set of odd numbers, then no even numbers would exist, hence the SET. But all these work as clarifying tools, and if you had read the thread you would have seen this definition provided also as regards mathematical sets and how they function.

But just for fun lets look at counting again, where does an infinite set for odd numbers begin????

We can pretend that there is no ending to the set as we might assumes time will never cease, unfortunately you have a beginning though, that would be a boundary.

"Sets" play a game with Time, not actual "things" or "object" in existence, we might say they exist potentially, but just not actually. As for hotels rooms, since nothing could exist beyond the infinite number of rooms, there would be nothing to add. Since Hilbert disregarded the definitive definition of boundlessness, He never even used an actually infinity as an example.

To clarify: 0 and 1(only), 0 is boundless in its nothingness, 1(only) is boundless in it's somethingness. Multiplicity cannot exist with Infinity.