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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.
Consider the endofunctor 1 + (−), i.e. F : Set → Set sending X to 1 + X, where 1 is a one-point set, a terminal object in the category. An algebra for this endofunctor is a set X (called the carrier of the algebra) together with a function f : (1 + X) → X. Defining such a function amounts to defining a point x ∈ X and a function X → X
In mathematics, an algebraic structure or algebraic system [1] consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.
In communications and electronic engineering, an intermediate frequency (IF) is a frequency to which a carrier wave is shifted as an intermediate step in transmission or reception. [1] The intermediate frequency is created by mixing the carrier signal with a local oscillator signal in a process called heterodyning , resulting in a signal at the ...
Elementary algebra, also known as high school algebra or college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 2 ] whilst algebra introduces variables (quantities without fixed values).
(where 1 denotes the identity map on A) gives exactly the definition of D being a derivation. Example: the Lie algebra of vector fields. Let A be the ring () of smooth functions on a smooth manifold X. Then a derivation of A over is equivalent to a vector field on X.
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