The ordered pair (70,20) as a set

A popular definition of an ordered pair (a,b) is the Kuratowski pair:

(a,b) = { { a }, { a, b } }

(70,20) = { { 70 }, { 70, 20 } }

Klick on one of the natural numbers to see how it is usually defined as a set.

This definition ensures the important properties of the pair, namely that the first and second element can be extracted and that (a,b) = (c,d) if and only if (a=c) and (b=d).

The ordered pair is used to define relations and functions: A relation is simply a set of ordered pairs - the relation holds between a and b if and only if (a,b) is in the set. A function is a relation where b₁=b₂ for all (a,b₁) and (a,b₂) in the relation (it has not more than one value b for a given a).

(back to √2)