Definition:Floor Function/Definition 3

Definition

Let $x$ be a real number.

The floor function of $x$ is the unique integer $\floor x$ such that:

$\floor x \le x < \floor x + 1$

Also see

• Real Number lies between Unique Pair of Consecutive Integers
• Equivalence of Definitions of Floor Function

Technical Note

The $\LaTeX$ code for \(\floor {x}\) is \floor {x} .

When the argument is a single character, it is usual to omit the braces:

\floor x

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 4$. Relations; functional relations; mappings: Example $4.8$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 10.4 \ \text{(i)}$: The well-ordering principle