Go backward to Theory of Reals
Go up to Top
Go forward to Real Numbers
Proposition: In R every non-negative number has an n-th root:
forall a in R >= 0, n in N>0: exists x in R: xn = a.
sqrtn(x) := such y: xn = y sqrt(x) := sqrt2N(x).
forall a in R >= 0, n in N>0: (sqrtn(a))n = a.
All roots of non-negative reals are well-defined.