Thread 16835630

If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and… then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities, and… (infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and…) continues forever. and that continues forever. and that continues forever. and that continues forever. and that continues forever. and…..(…)…

>>16835630 (OP)
Proof? I'm okay with an intuitive one but the existence of an infinity of infinities doesn't imply the existence of an infinity of infinity-infinites, does it?

Wait until you learn about the power set of the real numbers my nigga

>>16835630 (OP)
Set theory, once you study it, shows that some of the elements are infinity+infinity, some are infinity*infinity and some are infinity^infinity.
Furthermore, it shows that the different levels of infinity can be explored and that every instance of infinity+infinity and infinity*infinity stays on the same level. Only infinity^infinity can jump up a level.
.
If you start studying it, you can get to the technical details of this (ordinalities, cardinalities and measure) in less than a month.

>>16835734
i mean, if you already know the basics of functions (definition, domain, codomain, bijections, surjections, injections), cardinality is a topic that can be tackled in a week or less

>>16835630 (OP)
>If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and… then that must mean that there are not only infinite infinities, but an infinite number of those infinities
why?

>>16835630 (OP)
numbers are always finite you libtard