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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.
Definition:
sqrtn(x) := such y: xn = y sqrt(x) := sqrt2N(x).
Consequence:
forall a in R >= 0, n in N>0: (sqrtn(a))n = a.
All roots of non-negative reals are well-defined.