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Existence of nth Root via Induction by anomican is a document available to read on EtoBox.

This document proves by induction that any positive real number has an nth root. It first defines relevant concepts like the real numbers, nth root, and least upper bound axiom. It then proves for any positive a and integer n≥1, there exists an nth root of a. This is shown by induction on n, first proving the case for n=2 (square root exists), and then assuming the (n-1)th root exists to prove the nth root exists. It constructs a set with supremum x, relates x to another value y, and shows x must equal the

Author

anomican

Language

EN