ceilNk

CeilNk is a term encountered in mathematical and computational contexts that generally refers to the ceiling of a numeric expression labeled Nk. In standard interpretation, Nk is the product of two quantities N and k, and the notation ⌈Nk⌉ denotes the smallest integer greater than or equal to the product N·k. The meaning can vary with context, so careful definition is important when Nk is not explicitly a product.

If Nk is the product N·k with N and k real numbers, then ⌈Nk⌉ is the ceiling of that product. For integer values of N and k, Nk is already an integer, and ⌈Nk⌉ equals Nk. If either N or k is non-integer, the ceiling rounds Nk up to the nearest integer. A useful identity is ⌈x⌉ = -⌊-x⌋, which connects the ceiling to the floor function.

Ambiguity can arise in texts that use similar shorthand. Some authors might use Nk to denote a different quantity, such as a subscripted index or a special function, in which case ⌈Nk⌉ would be defined accordingly by the surrounding material. Therefore, the precise meaning of ceilNk depends on the conventions of the source.

Examples: if N = 4 and k = 1.5, Nk = 6 and ⌈Nk⌉ = 6. If N = 7 and k = -2.3, Nk = -16.1 and ⌈Nk⌉ = -16.

See also: Ceiling function, Floor function, Rounding.