real analysis
Also known as theory of functions of a real variable, theory of real functions
branch of mathematical analysis
Article
The least-upper-bound property (completeness) of the real numbers: that every non-empty bounded above subset has a supremum. Virtually every major theorem in real analysis relies on the completeness of the real numbers, including those concerning the existence of limits of sequences, the behaviour of continuous functions, and the existence and uniqueness of solutions to differential equations.
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