Axiom:Peano's Axioms/Historical Note

Historical Note on Peano's Axioms
A set of axioms on the same topic as Peano's axioms was initially formulated by in $1888$.

published them in $1889$ according to his own formulation, in a more precisely stated form than 's.

pointed out that while Peano's axioms give the key properties of the natural numbers, they do not actually define what the natural numbers actually are.

According to :


 * [These] assertions ... are known as the Peano axioms; they used to be considered as the fountainhead of all mathematical knowledge.

It is worth pointing out that the Peano axioms can be deduced to hold for the minimally inductive set as defined by the Axiom of Infinity from the Zermelo-Fraenkel axioms.

Thus they are now rarely considered as axiomatic as such.

However, in their time they were groundbreaking.