# Bound Variable/Examples/Existential Statement

Jump to navigation
Jump to search

## 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.

## Also see

## Sources

- 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: Where does this fit in?If you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*: $\S 2.1$