Are there an infinite number of infinities?



How many whole numbers are there? 

Infinity.



How many tenths of whole numbers are there?

Ten times infinity.



How many millionths of whole numbers are there?

1,000,000 times infinity.



How many decimal numbers are there?

Infinity times infinity.

finish middle school before visiting /sci/ pls

the word "cardinality" and the distinction between countably infinite (like whole/natural numbers) and uncountably infinite (like real numbers) should help your reading

meh, I didn't find Cantor until junior/senior year of HS

>>15368397 (OP)

>Are there an infinite number of infinities?

Depends on your axioms

>>15368397 (OP)

Maths is gay yes.

>hurr don't post about math until (((they))) have had the chance to indoctrinate you

>>15368397 (OP)

yes there are infinitely many infinities. start with the natural numbers, {0, 1, ... }. there's your first infinity. take the power set of that set - the set of all subsets. you can show there can be no bijection between a set and its powe set, no matter what set you start with. so this power set has a different infinite cardinality which, intuitively, must be bigger in some sense than the last. continue taking power sets and you get an infinite sequence of infinities.

Any math bros want to help me with this one?



Any circle has an infinite number of points. But some infinities are larger than others. 

A larger circle will have a larger infinity of points than a smaller circle.



Is this right so far?



Place the smaller circle within the larger circle.

Take the tangent from every point on the small circle and map them onto the corresponding point of the larger circle. 

You cant, right? Because the smaller circle will always have a smaller infinity of points than the bigger circle. 



But here's the problem for me. A point has no dimensions. Which means regardless of how closely you pack them together there is always room for more. Which in turn means that if you do the opposite, and try mapping all the points on the larger circle to the smaller circle, you can. 



Now, I just cant get my head around this apparent contradiction, can someone enlighten this poor retard?

>Take the tangent from every point on the small circle

My bad. I didn't mean tangent. I meant a line radiating directly outwards from the surface of the circle, an extension of the diameter. I dont what the proper term for such a line is called.

>>15368397 (OP)

Numbers are finite. Their ability to reproduce is irrelevant. Only a finite quantity can exist.

>>15368397 (OP)

Not when you can just put them all end to end in one set and condense all the infinities into a single infinity.

>Is this right so far?

No, all circles have infinite points.



>Take the tangent from every point on the small circle and map them onto the corresponding point of the larger circle.

>You cant, right?

You can't because there are infinite points, the process will never terminate, the only thing hindering you is the precision with which you can rotate the radial line because you can't actually rotate by an infinitesimal for infinite degrees of freedom in reality since your line will not be 0D thickness like the idealized points in the circle.

>Only a finite quantity can exist.

Then what is the finite quantity in 200 factorial or 1/0?

Also wtf are you talking about with numbers having the ability to reproduce?
