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Number systems include the familiar integers, rationals, reals, etc. as well as unusual extensions of these sets such as p-adic and hyperreal numbers.
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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.