ordered pair

"Relations" are what known in contemporary set theory as ordered pairs.

For some input ordered pairs, one of the below can be calculated.

Alternatively, an ordered pair can be formally thought of as a set with a total order.

The notation too is occasionally used for ordered pairs, especially in computer science.

It is evident that this mapping will cover all such ordered pairs.

There are many mathematical definitions of ordered pair which have this property.

For any ordered pair there are 4 symmetries fixing it.

These are typically written as an ordered pair (x, y).

The history of the notion of "ordered pair" is not clear.

But others view functions as simply sets of ordered pairs with unique first components.

In geometry, equipollence is a certain relationship between ordered pairs of points.

Given any two sets, their unordered and ordered pairs exist.

In a formal way, a data stream is any ordered pair where:

For any sets a and b, the ordered pair is defined by the following:

The chart is traditionally recorded as the ordered pair .

A general point in space-time is given by an ordered pair (x,t).

The elements of the disjoint union are ordered pairs (x, i).

Then A x B denotes the set of ordered pairs.

For each edge, the colors on the two vertices are restricted to some particular ordered pairs.

In the other definition a function is defined as a set of ordered pairs where each first element only occurs once.

The sum and difference of these ordered pairs are computed componentwise.

An -tuple is defined inductively using the construction of an ordered pair.

Relations are sets whose members are all ordered pairs.

A set of ordered pairs is a function if and only if .

Holmes (1998) takes the ordered pair and its left and right projections as primitive.