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The floor of x is also called the integral part, integer part, greatest integer, or entier of x, and was historically denoted [x] (among other notations). [2] However, the same term, integer part, is also used for truncation towards zero, which differs from the floor function for negative numbers. For n an integer, ⌊n⌋ = ⌈n⌉ = n.
In mathematics, an integer-valued function is a function whose values are integers.In other words, it is a function that assigns an integer to each member of its domain.. The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful.
Integer function may refer to: Integer-valued function, an integer function; Floor function, sometimes referred as the integer function, INT; Arithmetic function, a term for some functions of an integer variable
By consequence, we may get, for example, three different values for the fractional part of just one x: let it be −1.3, its fractional part will be 0.7 according to the first definition, 0.3 according to the second definition, and −0.3 according to the third definition, whose result can also be obtained in a straightforward way by
Denote by ⌊x⌋ the floor function of x (that is, the greatest integer less than or equal to x) and let {x} = x − ⌊x⌋ be the fractional part of x. There exists an integer k such that β k ≤ x < β k +1 .
Rounding is to the nearest integer—not necessarily to the nearest greater integer or nearest least integer. For example, 1.4 rounded is 1, the floor of 1.4 is 1, the ceiling of 1.4 is 2. 1.6 rounded is 2, the floor of 1.6 is 1, the ceiling of 1.6 is 2.
In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum , [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function.
For example: A rational function is a quotient of two polynomial functions, and is not defined at the zeros of the denominator. The tangent function is not defined for +, where k is any integer. The logarithm function is defined only for positive values of the variable.