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  2. Limit (category theory) - Wikipedia

    en.wikipedia.org/wiki/Limit_(category_theory)

    If the index category J is connected (and nonempty) then the unit of the adjunction is an isomorphism so that lim is a left inverse of Δ. This fails if J is not connected. For example, if J is a discrete category, the components of the unit are the diagonal morphisms δ : N → N J .

  3. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  4. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

  5. Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Central_limit_theorem

    In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution.

  6. Basel problem - Wikipedia

    en.wikipedia.org/wiki/Basel_problem

    The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]

  7. Nested intervals - Wikipedia

    en.wikipedia.org/wiki/Nested_intervals

    4 members of a sequence of nested intervals. In mathematics, a sequence of nested intervals can be intuitively understood as an ordered collection of intervals on the real number line with natural numbers =,,, … as an index.

  8. Cauchy–Hadamard theorem - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Hadamard_theorem

    In mathematics, the Cauchy–Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series.

  9. nth-term test - Wikipedia

    en.wikipedia.org/wiki/Nth-term_test

    In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series:. If or if the limit does not exist, then = diverges.. Many authors do not name this test or give it a shorter name.