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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 ...
The symbol is encoded in Unicode at U+221E ∞ INFINITY (∞) [25] and in LaTeX as \infty. [ 26 ] It was introduced in 1655 by John Wallis , [ 27 ] [ 28 ] and since its introduction, it has also been used outside mathematics in modern mysticism [ 29 ] and literary symbology .
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate , [ 1 ] after the lemniscate curves of a similar shape studied in algebraic geometry , [ 2 ] or "lazy eight", in the terminology of livestock branding .
It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose last quantifier is existential (e.g., "for all x, y, ... there exist(s) ..."). In the formal terms of symbolic logic , an existence theorem is a theorem with a prenex normal form involving the existential quantifier , even though in ...
Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many. "For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always ...
(the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols). ⊃ {\displaystyle \supset } may mean the same as ⇒ {\displaystyle \Rightarrow } (the symbol may also mean superset ).
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
which completes the proof that 3 is the unique solution of + =. In general, both existence (there exists at least one object) and uniqueness (there exists at most one object) must be proven, in order to conclude that there exists exactly one object satisfying a said condition.