Julius Wilhelm Richard Dedekind was a German mathematician who made important contributions to number theory, abstract algebra, and
the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as Logicism.
Richard Dedekind
Dedekind, before 1886
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.
The chain of light dominoes, starting with the nearest, can represent N, however, axioms 1–8 are also satisfied by the set of all light and dark dominoes. The 9th axiom (induction) limits N to the chain of light pieces ("no junk") as only light dominoes will fall when the nearest is toppled.