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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
by jgeralnik 8y 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.
- enedil 8y agoYes, 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.
- jgeralnik 8y agoTrue, 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"