# Definition:Open Statement

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## Definition

Let $P$ be a statement.

$P$ is an **open statement** if and only if $P$ contains at least one free occurrence of a variables that appears in it.

## Also known as

An **open statement** can also be seen referred to as an **open sentence**.

The word **formula** can also be seen.

## Examples

### Prime Number

The statement:

- $x$ is a prime number

is an open statement, as the variable $x$ appears as a free occurrence.

## Also see

## Sources

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 1$: Some mathematical language: Variables and quantifiers - 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**open sentence** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**open sentence**