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In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. [1]For example, if m and n are two logical matrices, then
In Boolean algebra, the inclusion relation is defined as ′ = and is the Boolean analogue to the subset relation in set theory.Inclusion is a partial order.. The inclusion relation < can be expressed in many ways:
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
The principle can be viewed as an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula. [ 4 ] As finite probabilities are computed as counts relative to the cardinality of the probability space , the formulas for the principle of inclusion–exclusion remain valid when the cardinalities ...
In mathematics, if is a subset of , then the inclusion map is the function that sends each element of to , treated as an element of ::, =. An inclusion map may also be referred to as an inclusion function , an insertion , [ 1 ] or a canonical injection .
A fuzzy subset A of a set X is a function A: X → L, where L is the interval [0, 1]. This function is also called a membership function. A membership function is a generalization of an indicator function (also called a characteristic function) of a subset defined for L = {0, 1}.
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For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".