Concept guide
Natural number: deciding membership through the smallest inductive set, and telling numbers from numerals
Under the OCME convention (0∈N), read the MKO's '0 and the numbers obtained from 0 by finitely many successor steps' as 'the smallest set of reals that contains 0 and is closed under x↦x+1'. On this basis prove 0∈N and 3∈N; show that the binary numeral '11' and the decimal numeral '3' denote the same natural number; prove −1∉N and 1/2∉N; and compare least elements with the convention N⁺=N∖{0}, in which natural numbers start at 1.