Number systems include the familiar integers, rationals, reals, etc. as well as unusual extensions of these sets such as p-adic and hyperreal numbers.
. . . . . .
Wikipedia: Number system
Fact archive: Number system
Construction -- Construction of sets of numbers, starting with the original Peano Axioms, formulated so that zero is included in the set of natural numbers. (See Is Zero a Natural Number?)
The webmaster and author of this Math Help site is Graeme McRae.