Complete Fields

Why

We want the a field which corresponds to points on the real line.¹

Definition

An ordered field² is complete if every nonempty subset bounded from above has a least upper bound.

1. Future editions are likely to modify this why. ↩︎
2. To be defined in future editions, but we take the usual definition of a field with an order. See, for example  Rational Order or Real Order). ↩︎