Counting quantification
Encyclopedia
A counting quantifier is a mathematical
term for a quantifier of the form "there exists at least k elements that satisfy property X".
In first-order logic
with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand.
However, they are interesting in the context of logics such as two-variable logic with counting that restrict the number of variables in formulas.
Also, generalized counting quantifiers that say "there exists infinitely many" are not expressible using a finite number of formulas in first-order logic.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
term for a quantifier of the form "there exists at least k elements that satisfy property X".
In first-order logic
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand.
However, they are interesting in the context of logics such as two-variable logic with counting that restrict the number of variables in formulas.
Also, generalized counting quantifiers that say "there exists infinitely many" are not expressible using a finite number of formulas in first-order logic.