Addition of Natural and Real Numbers

To prove the usual properties of addition, one must first define addition for the context in question. Addition is first defined on the natural numbers. In set theory, addition is then extended to progressively larger sets that include the natural numbers: the integers, the rational numbers, and the real numbers. (In mathematics education, positive fractions are added before negative numbers are even considered; this is also the historical route)

### Other articles related to "addition of natural and real numbers, real numbers, real number":

... Further information Construction of the real numbers A common construction of the set of real numbers is the Dedekind completion of the set of ... A real number is defined to be a Dedekind cut of rationals a non-empty set of rationals that is closed downward and has no greatest element ... The sum of real numbers a and b is defined element by element Define This definition was first published, in a slightly modified form, by Richard Dedekind in 1872 ...

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