Real_numbers

Real number axioms:

:Let R denote the set of real numbers, and w,x,y,z be elements of R. Then:

• The set R is a Field
• The field R is ordered i.e.
• if x >= y then x + z >= y + z
• if x >= 0 and y >= 0 then x * y >= 0
• If S is non-empty subset of R and S has an upper bound in R, then there exists some z in R that is a least upper bound for S.

A real number is one that can be expressed in the form

'DDD.ddd'.

• DDD is zero or more decimal digits
• ddd is zero or more decimal digits

Special cases:

• ddd is 0 - the format is 'DDD' and the decimal point is not included

Note: There are many subsets of the real numbers, including:

• Natural numbers
• Rational numbers
• Whole numbers
• (??? name) - infinitely repeating fractions (include in rational numbers???)
• (??? name) - infinitely long fractions that do not repeat (e.g., PI)

See also:

*Countably infinite