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Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam [1] (a Latin treatise circulated in France c. 1636 ) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus.
Formal equivalence is often more goal than reality, if only because one language may contain a word for a concept which has no direct equivalent in another language. In such cases, a more dynamic translation may be used or a neologism may be created in the target language to represent the concept (sometimes by borrowing a word from the source ...
In measure theory, a branch of mathematics, Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures.It gives an "if and only if" characterisation of when two such measures are equivalent, and hence it is extremely useful when trying to establish change-of-measure formulae for measures on function spaces.
In the category of sets, the coequalizer of two functions f, g : X → Y is the quotient of Y by the smallest equivalence relation ~ such that for every x ∈ X, we have f(x) ~ g(x). [1] In particular, if R is an equivalence relation on a set Y, and r 1, r 2 are the natural projections (R ⊂ Y × Y) → Y then the coequalizer of r 1 and r 2 is ...
Elementary equivalence; Equals sign; Equality (mathematics) Equality operator; Equipollence (geometry) Equivalence (measure theory) Equivalence class; Equivalence of categories; Equivalence of metrics; Equivalence relation; Equivalence test; Equivalent definitions of mathematical structures; Equivalent infinitesimal; Equivalent latitude ...
It may be the case that several sufficient conditions, when taken together, constitute a single necessary condition (i.e., individually sufficient and jointly necessary), as illustrated in example 5. Example 1 "John is a king" implies that John is male. So knowing that John is a king is sufficient to knowing that he is a male. Example 2
In 1964, [citation needed] Eugene Nida described translation as having two different types of equivalence: formal and dynamic equivalence. [14] Formal equivalence is when there is focus on the message itself (in both form and content); [ 15 ] the message in the target language should match the message in the source language as closely as ...
The canonical equivalence is given by the rule: "1" means "connected" (with an edge), "0" means "not connected". However, another rule, "0" means "connected", "1" means "not", may be used, and leads to another, natural but not canonical, equivalence. In this example, canonicity is rather a matter of convention. But here is a worse case.