Quantifier (logical)

The expressions “For all” and “There exists” used to formulate mathematical proposals in the Calcul of the predicates are called quantifications and the symbol which represents them in formal language is called a quantifier .

Universal quantification

The universal quantification is represented in mathematical notations by has with back (∀); it expresses " for tout" or " whatever the ".

For example, the assertion, expressed in natural language,

for any X, X satisfies the property P

state yourself formally:

∀x P (X)

The notation ∀ comes from German Alle .

Existential quantification

The existential quantification is represented by an E turned over (∃); it expresses " there exists un". This notation can be followed of one! what indicates the unicity of the element which follows, the significance becomes " then; there exists a unique"

for example, the assertion, expressed in natural language,

there exists X which satisfies the property P

state yourself formally:

∃x, P (X)

while

there exists single N, (follow-up of a predicate)

state yourself formally:

∃! N, follow-up of the prédicat'

The notation ∃ comes from German Existieren .

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