See quantifiable.

* * *

      in logic, the attachment of signs of quantity to the predicate or subject of a proposition. The universal quantifier, symbolized by (∀-) or (-), where the blank is filled by a variable, is used to express that the formula following holds for all values of the particular variable quantified. The existential quantifier, symbolized (∃-), expresses that the formula following holds for some (at least one) value of that quantified variable.

      Quantifiers of different types may be combined. For example, restricting epsilon (ε) and delta (δ) to positive values, b is called the limit of a function f(x) as x approaches a if for every ε there exists a δ such that whenever the distance from x to a is less than δ, then the distance from f(x) to b will be less than ε; or symbolically:

      in which vertical lines mark the enclosed quantities as absolute values, < means “is less than,” and ⊃ means “if . . . then,” or “implies.”

      Variables that are quantified are called bound (or dummy) variables, and those not quantified are called free variables. Thus, in the expression above, ε and δ are bound; and x, a, b, and f are free, since none of them occurs as an argument of either ∀ or ∃. See also propositional function.

* * *

Universalium. 2010.

Look at other dictionaries:

  • Quantification — has two distinct meanings.In mathematics and empirical science, it refers to human acts, known as counting and measuring that map human sense observations and experiences into members of some set of numbers. Quantification in this sense is… …   Wikipedia

  • quantification — [ kɑ̃tifikasjɔ̃ ] n. f. • mil. XIXe; en angl. 1840; → quantifier 1 ♦ Log. Détermination de la quantité (d un terme). Quantification du prédicat : selon Hamilton, attribution au prédicat d une extension indépendante de la qualité de la proposition …   Encyclopédie Universelle

  • Quantification — Quan ti*fi*ca tion, n. [See {Quantity}.] Modification by a reference to quantity; the introduction of the element of quantity. [1913 Webster] The quantification of the predicate belongs in part to Sir William Hamilton; viz., in its extension to… …   The Collaborative International Dictionary of English

  • quantification — theory …   Philosophy dictionary

  • quantification — index appraisal, measurement, rating Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • Quantification — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Sur les autres projets Wikimedia : « quantification », sur le Wiktionnaire (dictionnaire universel) En sciences, la quantification consiste …   Wikipédia en Français

  • quantification — quantify quan‧ti‧fy [ˈkwɒntfaɪ ǁ ˈkwɑːn ] verb quantified PTandPP [transitive] to measure something and express it as a number, especially something that is difficult to measure: • Quantifying the effect of advertising on sales is difficult.… …   Financial and business terms

  • quantification — kvantavimas statusas T sritis automatika atitikmenys: angl. quantification; quantization vok. Quantelung, f; Quantisieren, n; Quantisierung, f rus. квантирование, n; квантование, n pranc. quantification, f …   Automatikos terminų žodynas

  • quantification — kvantavimas statusas T sritis fizika atitikmenys: angl. quantification; quantization vok. Quantelung, f; Quantisierung, f rus. квантование, n pranc. quantification, f …   Fizikos terminų žodynas

  • quantification — quantify ► VERB (quantifies, quantified) ▪ express or measure the quantity of. DERIVATIVES quantifiable adjective quantification noun …   English terms dictionary

  • quantification — noun Date: circa 1840 the operation of quantifying • quantificational adjective • quantificationally adverb …   New Collegiate Dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”