File:Illustration_of_supremum.svg · Wikimedia Commons · See Wikimedia Commons
real analysis
Sign in to saveAlso known as theory of functions of a real variable, theory of real functions
branch of mathematical analysis
Wikidata facts
- Subclass of
- mathematical analysis
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- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- maintained by WikiProject
- WikiProject Mathematics
- topic's main category
- Category:Real analysis
- Stack Exchange tag
- mathoverflow.net/tags/real-analysis
- opposite of
- complex analysis
Sources (2)
via Wikidata · CC0
~40 min read
Encyclopedic overview
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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Excerpted from Wikipedia’s “real analysis” article, available under the CC BY-SA 4.0 licence.