Who formalized integer numbers?

I'm currently working on a thesis about Zermelo's axioms. In my first chapter I'm giving an introduction to the numerical treatment that Cantor gave to infinity.

When I was writing something about transfinite numbers as an expansion of natural numbers, I realized that I needed to include some reference to the formalization of numbers. I know that von Neumann gave the formal definition of natural number, but I couldn't find who formalized Integers ($$\mathbb{Z}$$).

Does anyone know who formalized integers, rationals, and reals? I know the construction as the palm of my hand but I don't know who did the great job.

Thanks in advance and may the health be with you!

• Peirce, Dedekind and Peano (who cited Dedekind) axiomatized natural numbers in 1880s, see Peano axioms. So did Frege, but his approach was not followed. The extension from natural numbers to integers, rationals and reals was known by then from the work of Weierstrass, Dedekind and Cantor. – Conifold Aug 22 '20 at 7:17
• Regarding the reals, three competing models were proposed in the late nineteenth century - the Weierstrass-Heine model using infinite decimal expansions; the Cantor-Heine-Meray model using Cauchy sequences; and the Dedekind model using his eponymous cuts. – Nick Aug 22 '20 at 16:45