(April 29, 2016 at 12:53 am)Alex K Wrote:(April 28, 2016 at 6:50 pm)dyresand Wrote: There is bigger numbers than infinity
"infinity" is not really a technical term for any particular (cardinal) number. If we are talking sizes of sets, both the natural and the real numbers have "infinite" size, but they are different infinities. The latter is larger than the former.
I wouldn't say larger, more like denser.
Like when I think about comparing infinites, I cut up both the infinites equally. Like,set of natural numbers cut up at 5. And the set of real numbers cut up at 5. So when we look at it the cut up version of the real numbers will have more numbers than the cut up version of natural numbers.
Like the cut up version of natural numbers will only have 1,2,3,4,5 whereas the cut up version of real numbers will have 1,2,3,4,5 and ever other number between them. So I think all infinities are equal in size but different in density. Like according to my example set of real numbers and natural numbers would be equal in size but different in density, like the set of real numbers would be infinitely denser than set of natural numbers.
Does that make any sense? Lol