Definition:Floor Function/Also known as

Floor Function: Also known as

The floor function of a real number $x$ is usually just referred to as the floor of $x$.

The floor function is sometimes called the entier function, from the French for integer.

The floor of $x$ is also often referred to as the integer part or integral part of $x$, particularly in older treatments of number theory.

Some sources give it as the greatest integer function.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): Chapter $2$. Equivalence Relations: Exercise $3$
• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 1.4$: Decomposition of a set into classes. Equivalence relations: Example $3$ (footnote $4$)
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 10$: The well-ordering principle
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 20 \ (1)$: Introduction
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): greatest integer function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): floor function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integer part
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): floor function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): greatest integer function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integer part
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): greatest integer function (floor)