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Completeness of the real numbers

Every nonempty real set bounded above has a least upper bound.

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More concepts to explore

  • Bolzano–Weierstrass theorem

    Every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence.

  • Continuity

    Continuity at a point means that the function value equals its limit there; continuity on an interval requires this at each relevant point.

  • Quantifiers

    Universal and existential quantifiers specify how a statement ranges over a domain.

  • Sequence convergence

    A sequence converges when its terms eventually lie within every prescribed distance of a limit.

  • Cauchy sequences

    Terms of a Cauchy sequence eventually become arbitrarily close to each other.

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Mathematical and Real Analysis

Explore real numbers and limits; continuity and compactness; functions and integration. Concepts and connections are available independently of video coverage.

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