Hacker News new | ask | show | jobs
by jgeralnik 2884 days ago
Not quite, you can't order all natural numbers alphabetically either but that doesn't mean you can't count them.

A better way to count based on names would be to first count all single letter names alphabetically, then all two letter names alphabetically, etc.
1 comments
enedil 2884 days ago
Yes, you can. Order is just a relation, i.e. a set that contains pairs of elements. So for example, let X be the relation <. X is a subset of NxN, the cartesian product of N. We say that n<m if the pair (n,m) is in X. Moreover, we say that (n,n+1) is in X, and whenever (n,m) in X and (m,k) in X, then (n,k) in X. This constitues order on naturals.
link
jgeralnik 2870 days ago
True, but the GP claimed that if we can order alphabetically we can create a one to one correspondence with natural numbers.

Obviously we can order reals (using <), I interpreted the original post as referring not to your definition but to "order and count"

link