Real numbers are completely characterized by their fundamental properties that can be summarized by saying that they form an ordered field that is See more

Previous properties do not distinguish real numbers from rational numbers. This distinction is provided by Dedekind completeness, … See more

A main reason for using real numbers is so that many sequences have limits. More formally, the reals are complete (in the sense of metric spaces or uniform spaces, which is a different … See more

As a topological space, the real numbers are separable. This is because the set of rationals, which is countable, is dense in the real numbers. The irrational numbers are also dense in the … See more

The real numbers form an ordered field. Intuitively, this means that methods and rules of elementary arithmetic apply to them. More precisely, there are two binary operations See more

The most common way of describing a real number is via its decimal representation, a sequence of decimal digits each representing the product of an integer between zero … See more

The set of all real numbers is uncountable, in the sense that while both the set of all natural numbers {1, 2, 3, 4, ...} and the set of all real numbers are infinite sets, there exists no one-to-one function from the real numbers to the natural numbers. The cardinality See more