Editing Ordered Pairs in set

= Ordered Pairs - Definition and Examples =

An '''ordered pair''' is a fundamental concept in mathematics used to represent two elements together with an order that matters. It is usually written as <math>(a, b)</math>, where <math>a</math> is called the '''first element''' and <math>b</math> is the '''second element'''.

== Key Points ==

* Unlike sets, the order of elements in an ordered pair is important.  
* Two ordered pairs <math>(a, b)</math> and <math>(c, d)</math> are equal if and only if <math>a = c</math> and <math>b = d</math>.  
* Ordered pairs are used to define relations and functions in mathematics.

== Examples ==

1. Consider the ordered pair <math>(2, 5)</math>. Here, 2 is the first element and 5 is the second element.  
2. The ordered pair <math>(3, 7)</math> is not the same as <math>(7, 3)</math>, because the order of elements is different.  
3. If <math>A = \{1, 2\}</math> and <math>B = \{3, 4\}</math>, then the ordered pair <math>(1, 3)</math> is different from <math>(3, 1)</math>.

== Usage ==

Ordered pairs are used in coordinate geometry to represent points on the plane, such as <math>(x, y)</math>, where <math>x</math> is the horizontal coordinate and <math>y</math> is the vertical coordinate.

[[Category:Set Theory]]
[[Category:Mathematics]]