Ordered pair
Date: 2025-12-13
An ordered pair is a pair of elements where one element is considered "next" to the other
The elements of a pair can belong to different sets
(a,c) is the notation for the ordered pair of a and c.
A pair can be defined using two selector functions
Let l and r be functions where l chooses the left element of a pair and r chooses the right one
Thus, l and r are functions such that:
l (a,c) → a
r (a,c) → c
Since we use left-side order notation, (a,c) is l-ordered and (c,a) is r-ordered respectively
Example
In chess, we have a set of files(columns) {a,b,c,d,e,f,g,h} and a set of ranks(rows) {1,2,3,4,5,6,7,8}.
Let f be an indicator function that checks if a square is empty or occupied by a piece.
f:X→{empty,piece},where X is the set of all pairs from (a,1) to (h,8), i.e. the set of all squares
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