Explain different types of infinity to me, /sci/.

>>8048797
Assume the axiom of infinite. You now have a valid system for saying two infinite sets have different cardinality.

You can also assume the logical opposite and the logic will still work.

>>8048804
So, in theory, one could assume that literally every conceivable thing exists, due to the nature of infinity?

>>8048804
>axiom of infinity

>>8048797
There are countable infinities, such as the real numbers. You could list them, even though it's an infinitely long list. 1, 2, 3.....
Then there are uncountable infinities, such as the quantity of decimal numbers between 0 and 1. You could never write them in a list, you could never know where to start after 0. Is the next number in that list 0.000000001? Or 0.000000000000000000001? You will never be able to list the next number.
Countable and uncountable infinities are two types I believe, and there are more complex types which fall into one of those two categories.

>>8048809
I think your first sentence should be
>There are countable infinities, such as the Natural numbers

>>8048809
>You could list them
This is left as an exercise to the reader

File: 3453.jpg (116KB, 532x800px) Image search: [Google]

116KB, 532x800px

Infinity: The inability for a fundamental part to decay into smaller parts, thus rendering it infinite in lifetime.

>>8048806
1. That isn't the axiom of infinity.
2. That has nothing to do with the axiom of infinity.
3. That has nothing to do with ZFC, from which the axiom of infinity comes.
4. That has nothing to do with math at all.
5. That has nothing to do with infinity.
6. No. Not even in theory.

>>8048797
Well there's + and -

>>8048814
Yeah you're absolutely right thanks for the correction

How can real numbers be more than rational numbers if there's always a rational between two reals? this shit is driving me stupid

>>8048797
infinite hotel vid from [spoiler]tedx[/spoiler] is actually pretty good

https://www.youtube.com/watch?v=Uj3_KqkI9Zo

>>8048988
\infty=-\infty

>>8050363
Because there is no bijection between the natural numbers and the real numbers.

>>8050363
Because there are more infinitely long continued fractions than there are finite continued fractions.

OR SO WE THINK. Look up the continuum hypothesis.