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  2. Limit (mathematics) - Wikipedia

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

    Augustin-Louis Cauchy in 1821, [6] followed by Karl Weierstrass, formalized the definition of the limit of a function which became known as the (ε, δ)-definition of limit. The modern notation of placing the arrow below the limit symbol is due to G. H. Hardy, who introduced it in his book A Course of Pure Mathematics in 1908. [7]

  3. Inverse limit - Wikipedia

    en.wikipedia.org/wiki/Inverse_limit

    The inverse limit of this system is an object X in C together with morphisms π i: X → X i (called projections) satisfying π i = ∘ π j for all i ≤ j. The pair ( X , π i ) must be universal in the sense that for any other such pair ( Y , ψ i ) there exists a unique morphism u : Y → X such that the diagram

  4. Limit (category theory) - Wikipedia

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

    A functor G : C → D is said to lift limits for a diagram F : J → C if whenever (L, φ) is a limit of GF there exists a limit (L′, φ′) of F such that G(L′, φ′) = (L, φ). A functor G lifts limits of shape J if it lifts limits for all diagrams of shape J. One can therefore talk about lifting products, equalizers, pullbacks, etc.

  5. Detection limit - Wikipedia

    en.wikipedia.org/wiki/Detection_limit

    These include the instrument detection limit (IDL), the method detection limit (MDL), the practical quantitation limit (PQL), and the limit of quantitation (LOQ). Even when the same terminology is used, there can be differences in the LOD according to nuances of what definition is used and what type of noise contributes to the measurement and ...

  6. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    The definition of limit given here does not depend on how (or whether) f is defined at p. Bartle [9] refers to this as a deleted limit, because it excludes the value of f at p. The corresponding non-deleted limit does depend on the value of f at p, if p is in the domain of f. Let : be a real-valued function.

  7. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    supremum = least upper bound. A lower bound of a subset of a partially ordered set (,) is an element of such that . for all .; A lower bound of is called an infimum (or greatest lower bound, or meet) of if

  8. Mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_analysis

    Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense.

  9. Monotonic function - Wikipedia

    en.wikipedia.org/wiki/Monotonic_function

    Figure 1. A monotonically non-decreasing function Figure 2. A monotonically non-increasing function Figure 3. A function that is not monotonic. In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.