ChainCountry code: us, country type: geoip, valid: 1 No.25281
In constructive mathematics, $2^{\mathbb{N}}$ differs fundamentally from $\powerset(\mathbb{N})$: functions from ℕ to 2 represent decidable subsets, while the powerset of ℕ consists of all predicates on ℕ, which need not be decidable. Classically they're isomorphic via characteristic functions, but constructively that isomorphism breaks down because not every subset can be decided.
Source: Claude