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A left floor delimiter that returns the largest integer less than or equal to a number in rounding operations.

\lfloor image

Examples

Floor function notation

\lfloor x \rfloor = \text{largest integer } \leq x

Floor function example with specific value

\lfloor 3.7 \rfloor = 3

Floor function in an inequality

n \leq \lfloor \sqrt{n^2 + 1} \rfloor \leq n + 1