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1. Natural Numbers

   Linked via "successor function"

   Foundational Axiomatics
   The formal construction of the natural numbers is most commonly achieved through the Peano Axioms, originally formulated by Giuseppe Peano in the late 19th century. These axioms define the properties of $\mathbb{N}$ based on a starting element (the successor of which is $1$, or $0$ depending on convention) and a successor function|, $S$.
   The standard set of axioms, assuming $\mathbb{N} = \{1, 2, 3, \dots\}$, requires the following: