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A binary operation is a binary function where the sets X, Y, and Z are all equal; binary operations are often used to define algebraic structures. In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f x and f y are all linear transformations.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation on a set is a binary function whose two domains and the codomain are the same set.
There are two common types of operations: unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. [3] Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation. [4] Operations can involve mathematical objects other than ...
In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra "2" has some following in the literature, and will be employed here.
When a commutative operation is written as a binary function = (,), then this function is called a symmetric function, and its graph in three-dimensional space is symmetric across the plane =. For example, if the function f is defined as f ( x , y ) = x + y {\displaystyle f(x,y)=x+y} then f {\displaystyle f} is a symmetric function.
The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as f ( x ) = x 2 {\displaystyle f(x)=x^{2}} , is called a unary function .
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