Theorem: For every +ve real x and every +ve integer n, there exist a real y such that y power n = x

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For all x ≥ 0, there exists n ﹥ 0 such that n-1 ≤ x ﹤ n (Proof) [ILIEKMATHPHYSICS]

For all x ﹥ 0, there exists n ﹥0 such that 0 ﹤ 1/n ﹤ x (Proof) [ILIEKMATHPHYSICS]

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Prove for all x in R, there is a unique n in Z such that n-1 ≤ x ﹤ n (Proof)

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The Euler Formula