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In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Any equivalence relation is the negation of an apartness relation, though the converse statement only holds in classical mathematics (as opposed to constructive mathematics), since it is equivalent to the law of excluded middle. Each relation that is both reflexive and left (or right) Euclidean is also an equivalence relation.
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [ 1 ] [ 2 ] Equality between A and B is written A = B , and pronounced " A equals B ".
A term's definition may require additional properties that are not listed in this table. A homogeneous relation R on the set X is a transitive relation if, [ 1 ] for all a , b , c ∈ X , if a R b and b R c , then a R c .
In mathematics, a binary relation associates elements of one set called the domain with elements of another set called the codomain. [1] Precisely, a binary relation over sets X {\displaystyle X} and Y {\displaystyle Y} is a set of ordered pairs ( x , y ) {\displaystyle (x,y)} where x {\displaystyle x} is in X {\displaystyle X} and y ...
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
A term's definition may require additional properties that are not listed in this table. In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all distinct pairs of elements of the set in one direction or the other while it is called strongly connected if it relates all pairs of elements.