5 ms·
Stranger still is that one can find a rational number between any two irrational numbers, yet the irrationals vastly outnumber (are not countably infinite) the
by z5h 5y ago
Stranger still is that one can find a rational number between any two irrational numbers, yet the irrationals vastly outnumber (are not countably infinite) the rationals (which are countably infinite).
Cantor’s diagonal argument is an easy foray into uncountable cardinalities https://en.m.wikipedia.org/wiki/Cantor's_diagonal_argument https://en.m.wikipedia.org/wiki/Cantor's_diagonal_argument
- TchoBeer 5y agoWhen I was much younger this was the source of a lot of wonder for me. Both the rationals and the irrationals are dense in the reals, and yet the irrationals greatly outnumber the rationals.