Re:How can some infinities be bigger than others?
by thfuran on Wednesday April 19, 2023 @06:37PM
(#35634197)
>For any infinite set, you could select unique values out of them indefinitely.
Yes, but if you have a bijection between elements of that set and another, they're still the same size. Consider the strictly positive integers and the strictly negative integers: for any x, there's a corresponding -x. There are infinite elements in both sets, but they're the same size. Contrast that with, for example, the reals and the natural numbers: for each natural number n, there's not a corresponding real number but rather an infinite number of reals in [n, n+1). The sets are not the same size.
Yes, but if you have a bijection between elements of that set and another, they're still the same size. Consider the strictly positive integers and the strictly negative integers: for any x, there's a corresponding -x. There are infinite elements in both sets, but they're the same size. Contrast that with, for example, the reals and the natural numbers: for each natural number n, there's not a corresponding real number but rather an infinite number of reals in [n, n+1). The sets are not the same size.