Existential quantification

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'. Some sources use the term existentialization to refer to existential quantification. 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)'). Existential quantification is distinct from universal quantification ('for all'), which asserts that the property or relation holds for all members of the domain.0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, and so on.For some natural number n, n·n = 25.For some positive odd number n, n·n = 25 For some natural number n, n is odd and n·n = 25.For some natural number n, n·n = 25.For some natural number n, n is even and n·n = 25. 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'. Some sources use the term existentialization to refer to existential quantification. 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)'). Existential quantification is distinct from universal quantification ('for all'), which asserts that the property or relation holds for all members of the domain. Consider a formula that states that some natural number multiplied by itself is 25. This would seem to be a logical disjunction because of the repeated use of 'or'. However, the 'and so on' makes this impossible to integrate and to interpret as a disjunction in formal logic.Instead, the statement could be rephrased more formally as