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Ceiling Function

Ceiling Function
Least Integer Function

A step function of x which is the least integer greater than or equal to x. The ceiling function of x is usually written Ceiling function notation: [x] with left brackets reversed, denoting the least integer greater than or equal to x.. Sometimes this function is written with reversed floor function brackets Mathematical notation showing the ceiling function symbol: ⌈x⌉ (x enclosed between reversed floor brackets), and other times it is written with reversed boldface brackets ]x[ or reversed plain brackets ]x[.

Examples: Ceiling function notation: [4.9] = 5, showing the least integer greater than or equal to 4.9 equals 5. and Ceiling function example: ⌈-4.9⌉ = -4, showing the least integer greater than or equal to -4.9.

 

Graph of y = ⌈x⌉ (ceiling function), showing horizontal steps with open left endpoints and closed right endpoints across all...

 

See also

Floor function (also called greatest integer function)