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What is an ordered pair?

What is an ordered pair? Here are some definitions.

Noun
  1. (set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or
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Examples
Once you have determined the co-ordinates of a point, you can label the points using ordered pair notation.
The holes centres in parts are determined in a plane, in a two-dimensional space by an ordered pair of real numbers.
Functions can be defined by the ordered pair notation, tables, or graphs.
A simple illustration of explication is provided by the definition of ordered pair in set theory.
In linear algebra, an ordered pair of numbers typically represents a vector, which in the present setting of coordinates can be taken to mean a change in location.

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