PROOF Infinite Nested CUBE Root Makes Sense! | Real Analysis for Beginners!

Описание: We prove that the expression expressed in words as "the cube root of 1 plus the cube root of 1 plus the cube root of 1 plus ..." - an infinite nested radical where the radicals are cube roots - makes sense and is actually a well-defined real number. The proof is based on expressing the infinite nested radical as the limit of a bounded increasing sequence of real numbers. We define the number as the limit of a recursively defined sequence, and we prove by mathematical induction that the sequence is bounded and increasing. The completeness of the real numbers implies that the sequence has a limit, which is the well-defined value of the infinite nested cube root.

The video is designed for people interested in learning mathematical proofs and proof techniques (such as proof by induction), as well as people interested in learning important beginner ideas from real analysis.

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