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  2. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    There is a corresponding greatest-lower-bound property; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least ...

  3. Limit inferior and limit superior - Wikipedia

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

    Thus, the infimum or meet of a collection of subsets is the greatest lower bound while the supremum or join is the least upper bound. In this context, the inner limit, lim inf X n, is the largest meeting of tails of the sequence, and the outer limit, lim sup X n, is the smallest joining of tails of the sequence. The following makes this precise.

  4. Template:Calculus - Wikipedia

    en.wikipedia.org/wiki/Template:Calculus

    Download as PDF; Printable version; ... Euler's formula; Partial fractions ... Template:Calculus is used to give a brief outline of calculus topics ...

  5. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    Likewise, a greatest element of a partially ordered set (poset) is an upper bound of the set which is contained within the set, whereas the maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A), then m = b. Any least element or greatest element of a poset is unique, but a poset can have several minimal or ...

  6. Join and meet - Wikipedia

    en.wikipedia.org/wiki/Join_and_meet

    If (,) is a partially ordered set, such that each pair of elements in has a meet, then indeed = if and only if , since in the latter case indeed is a lower bound of , and since is the greatest lower bound if and only if it is a lower bound. Thus, the partial order defined by the meet in the universal algebra approach coincides with the original ...

  7. Max–min inequality - Wikipedia

    en.wikipedia.org/wiki/Max–min_inequality

    By the greatest lower bound property of infimum, () (). Putting all the pieces together, we get Putting all the pieces together, we get sup z ∈ Z inf w ∈ W f ( z , w ) = sup z ∈ Z g ( z ) ≤ inf w ∈ W h ( w ) = inf w ∈ W sup z ∈ Z f ( z , w ) {\displaystyle \sup _{z\in Z}\inf _{w\in W}f(z,w)=\sup _{z\in Z}g(z)\leq \inf _{w\in W}h(w ...

  8. Lattice (order) - Wikipedia

    en.wikipedia.org/wiki/Lattice_(order)

    A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

  9. Limits of integration - Wikipedia

    en.wikipedia.org/wiki/Limits_of_integration

    In calculus and mathematical analysis the limits of integration (or bounds of integration) of the integral () of a Riemann integrable function f {\displaystyle f} defined on a closed and bounded interval are the real numbers a {\displaystyle a} and b {\displaystyle b} , in which a {\displaystyle a} is called the lower limit and b {\displaystyle ...

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