I know what it means to talk about the ordinal "ω + 1" || The natural numbers are
@ciphergoth yes || ambiguous because different people have different meanings, so I always say "positive integers" or "nonnegative integers" depending on which one I happen to need to talk about
@ciphergoth I literally have no opinion on that! I never use the term "natural numbers"; I always write ℤ˲₀ or ℤ˲₌₀ and say "positive" or "nonnegative"; I am equally comfortable understanding someone else's usage whichever convention they use.