- Not every element has a square root in Q:
- ~exists x: x*x = 2.
- sqrt(x) := such z: x = z*z.
- sqrt(2) is undefined.
- Proof: see lecture notes.
- Introduce a set R of real numbers such that
- Q can be "embedded" into R, and
- for every non-negative
real number a there is a real number x
with a = x*x (and consequently sqrt(a)
Author: Wolfgang Schreiner
Last Modification: November 16, 1999