more from Herbert B. Enderton

Single Idea 13204

[catalogued under 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST]

Full Idea

The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used.

Gist of Idea

The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}


Herbert B. Enderton (Elements of Set Theory [1977], 3:36)

Book Reference

Enderton,Herbert B.: 'Elements of Set Theory' [Posts + Telecoms 2006], p.36

A Reaction

This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation.