4 ms·
“Countable” as used in mathematics does not necessarily imply finite. The integers are “countably infinite”, and so is anything you can put in a 1:1 corresponde
by titanomachy 2y ago
“Countable” as used in mathematics does not necessarily imply finite. The integers are “countably infinite”, and so is anything you can put in a 1:1 correspondence with integers.
- gcanyon 2y agoBut as I said, if programs are of infinite length, then a diagonalization argument proves the computable numbers not to be countable I think.
- titanomachy 2y agoAh yes, of course you're right. I think it does make sense to assume the programs are finite, I don't think numbers described by an infinite program should be considered computable.