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In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!"
(the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols). ... there exists, for some first-order logic
The corresponding symbol for the existential quantifier is "∃", a rotated letter "E", which stands for "there exists" or "exists". [ 1 ] [ 2 ] An example of translating a quantified statement in a natural language such as English would be as follows.
The negation of the sentence "For every x, if x is a philosopher, then x is a scholar" is logically equivalent to the sentence "There exists x such that x is a philosopher and x is not a scholar". The existential quantifier "there exists" expresses the idea that the claim "x is a philosopher and x is not a scholar" holds for some choice of x.
The ∈ symbol here denotes set membership, ... The ∃ sign stands for "there exists", which is known as existential quantification. So for example, ...
In logic, a logical constant or constant symbol of a language is a symbol that has the same ... "there exists", "for some" = "equals"
In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.