Search results
Results From The WOW.Com Content Network
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
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
In mathematics, Hermite's identity, named after Charles Hermite, gives the value of a summation involving the floor function. It states that for every real number x and for every positive integer n the following identity holds: [ 1 ] [ 2 ]
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.
For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly.
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
Conversions to integer are not intuitive: converting (63.0/9.0) to integer yields 7, but converting (0.63/0.09) may yield 6. This is because conversions generally truncate rather than round. Floor and ceiling functions may produce answers which are off by one from the intuitively expected value.