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...(..)...

ok

babby's first set theory

>>16720262
This retarded Venn diagram says there are real numbers that are neither rational nor irrational.

>>16720265
Yes

>>16720272
what are those? transcendental? random?

>>16720272
That isn't possible by definition of any irrational number being a number which is not rational.

>>16720130 (OP)
now you understand why finitism is a thing, and why it makes so many mathematicians seethe

>>16720130 (OP)
An infinite number of sets walk into a bar. The bar immediately turns into the set of all sets and all the sets inside the bar are killed because of the principle of explosion. A mysterious entity outside the bar remarks, "how unclassy!"

>>16720319
we dont use the excluded middle assumption here saar

>>16720277
one needs to drop the law of the excluded middle to find them, it one of intuitionism's best kept secrets