Ordered pair

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Definition: Ordered pair
If [math]x [/math] and [math]y [/math] are things, then [math](x,y) [/math] is the ordered pair of [math]x [/math] and [math]y [/math].


Two ordered pairs [math](x_1,y_1) [/math] and [math](x_2,y_2) [/math] are equal if [math]x_1 = x_2 [/math] and [math]y_1 = y_2 [/math].

In particular, order matters: [math](1,2) \neq (2,1) [/math] because [math]1 \neq 2 [/math].

We can also consider ordered triples, quadruples, etc. The general term is a k-tuple. For example, a pair is a 2-tuple and a triple is a 3-tuple.