Definition:Existential Statement
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Definition
An existential statement is one which expresses the existence of at least one object (in a particular universe of discourse) which has a particular property.
That is, a statement of the form:
- $\exists x: P \left({x}\right)$
where:
- $\exists$ is the existential quantifier;
- $P$ is a predicate symbol.
It means:
- There exists at least one $x$ (in some given universe of discourse) which has the property $P$.
Also see
Dummy Variable
In the expression $\exists x: P \left({x}\right)$, the symbol $x$ is known as a dummy variable, or bound variable.
Thus, the meaning of $\exists x: P \left({x}\right)$ does not change if $x$ is replaced by another symbol.
That is, $\exists x: P \left({x}\right)$ means the same thing as $\exists y: P \left({y}\right)$ or $\exists \alpha: P \left({\alpha}\right)$. And so on.
