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1. Natural Numbers

   Linked via "Axiom of Induction"

   $1$ is not the successor of any natural number.
   If $S(m) = S(n)$, then $m = n$ (the successor function (injective)/)).
   The Axiom of Induction: If a property $P$ is true for $1$, and if the truth of $P$ for any number $k$ implies the truth of $P$ for $S(k)$, then $P$ is true for all natural numbers.
   The necessity of the induction axiom is deeply related to the concept of infinity, as it is the formal mechanism that ensures that no non-natural element can be constructed through finite ap…