4 ms·
There are different kinds of infinity. The integers are countable, the real numbers aren't. You can prove that if you try to map each integer to some rational n
by jimm 10y ago
There are different kinds of infinity. The integers are countable, the real numbers aren't. You can prove that if you try to map each integer to some rational number, there will be some rational numbers that are not on that list --- there are more of them. See https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument.
- wutbrodo 10y ago> You can prove that if you try to map each integer to some rational number, there will be some rational numbers that are not on that list --- there are more of them. Did you mean reals here? There _is_ a (bijection) mapping between integers and rationals. https://en.wikipedia.org/wiki/Cantor_pairing_function#Cantor_pairing_function https://en.wikipedia.org/wiki/Cantor_pairing_function#Cantor...