Bound Variable/Examples/Universal Statement

Example of Bound Variable

In the universal statement:

$\forall x: \map P x$

the symbol $x$ is a bound variable.

Thus, the meaning of $\forall x: \map P x$ does not change if $x$ is replaced by another symbol.

That is, $\forall x: \map P x$ means the same thing as $\forall y: \map P y$ or $\forall \alpha: \map P \alpha$.

And so on.


Also see


Sources

  • 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers
  • 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic
  • 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability: $\S 2.1$
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