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Existence of Real Roots

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.