A set of ordered pairs is a relation. Or Just simply "Coordinates"
Usually the set of x values.
A relation is defined as a set of tuples. Mathematically, elements of a set have no order among them; hence, tuples in a relation do not have any particular order. In other words, a relation is not sensitive to the ordering of tuples. Tuple ordering is not part of a relation definition because a relation attempts to represent facts at a logical or abstract level. Many logical orders can be specified on a relation but there is no preference for one logical ordering over another.
It is the set on which the relation is defined to the set which is known as the range.
A relation doesn't have an "output value", in the sense that a function does. A set of values is either part of the relation, or it isn't.
they are the first set of paired elements
The relation, between two sets of objects, is a mapping which associates elements of the first set to those of the second set.
An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.
Elements belong to subsets: subsets contain elements (from the parent set).
A relation is a mapping from one set to another. It is a function if elements of the first set are mapped to only one element from the second set. So, for example, square root is not a function because 9 can be mapped to -3 and 3.
A relation is a mapping from elements of one set, called the domain, to elements of another set, called the range. The function of the three terms: relation, domain and range, is to define the parameters of a mapping which may or may not be a function.
Since relation is a set, and tuples are element of a set, according to set theory, the elements of a set are not ordered.
If the universal set, U, has N elements then it has 2N subsets.
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A set of ordered pairs is a relation. Or Just simply "Coordinates"
2^(n^2+n)/2 is the number of symmetric relations on a set of n elements.
2^32 because 2^(n*(n+1)/2) is the no of symmetric relation for n elements in a given set