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For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.
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]
For example, += and -= are often called plus equal(s) and minus equal(s), instead of the more verbose "assignment by addition" and "assignment by subtraction". The binding of operators in C and C++ is specified (in the corresponding Standards) by a factored language grammar, rather than a precedence table. This creates some subtle conflicts.
The type-generic macros that correspond to a function that is defined for only real numbers encapsulates a total of 3 different functions: float, double and long double variants of the function. The C++ language includes native support for function overloading and thus does not provide the <tgmath.h> header even as a compatibility feature.
In the above theorem, each of the four integers has a name of its own: a is called the dividend, b is called the divisor, q is called the quotient and r is called the remainder. The computation of the quotient and the remainder from the dividend and the divisor is called division, or in case of ambiguity, Euclidean division.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
For example, density (mass divided by volume, in units of kg/m 3) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". [8] Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size".
The function: / sending a in A to its equivalence class a + B is called the quotient map or the projection map, and is a module homomorphism. The addition operation on A / B is defined for two equivalence classes as the equivalence class of the sum of two representatives from these classes; and scalar multiplication of elements of A / B by ...