Natural numbers: Difference between revisions

The natural numbers are fundamental objects in mathematics, and thus different areas of math have different conventions of encoding or defining them. In many areas such as geometry or number theory, they are taken as primitives and not formally treated

During the early development of foundational philosophy and logicism, [[:wikipedia:Gottlob Frege|Gottlob Frege]] and [[:wikipedia:Bertrand Russell|Bertrand Russell]] proposed defining a natural number \( n \) as the equivalence [[class]] of all sets with [[cardinality]] \( n \). This definition cannot be realized in ZFC, because the classes involved are [[proper class]]es, except for \( n = 0 \).