Bound Variable/Examples/Existential Statement
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Example of Bound Variable
In the existential statement:
- $\exists x: \map P x$
the symbol $x$ is a bound variable.
Thus, the meaning of $\exists x: \map P x$ does not change if $x$ is replaced by another symbol.
That is, $\exists x: \map P x$ means the same thing as $\exists y: \map P y$ or $\exists \alpha: \map P \alpha$. And so on.
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers
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- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability: $\S 2.1$