Somebody sent me an email with the following comment on the entry *countable set*. I am not in position to react to this, maybe some expert here could reply. The sentence being quoted originates from revision 1 of the entry.

Forwarded message:

]]>“We do have, however, that a countable set is either empty or inhabited, which is classically trivial but need not hold constructively for every set.”

(https://ncatlab.org/nlab/show/countable+set)

The set D={n\in N | 2n+6 is not the sum of two odd primes} is decidable, hence countable. However we cannot decide whether it is empty or inhabited. (We could decide it if we assumed LPO, for instance.)

Do you agree?