June 14, 2021July 1, 2021

Existence of nth Roots of Positive Reals

The Completeness Axiom helps us prove the existence of nth roots of positive real numbers, but the proof is quite challenging.

Real Analysis Study Help for Baby Rudin, Part 1.6

The existence of nth roots, including the square root of two, is ultimately based on the continuity of power functions with positive integer exponents. — Ultimately, the continuity of $f(x)=x^{2}$ at $x=\sqrt{2}$ allows us to prove the existence of $\sqrt{2}$ . Later, the argument is based on the Intermediate Value Theorem. In this article, the argument is

f(x)=x^{2} — Ultimately, the continuity of $f(x)=x^{2}$ at $x=\sqrt{2}$ allows us to prove the existence of $\sqrt{2}$ . Later, the argument is based on the Intermediate Value Theorem. In this article, the argument is

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January 7, 2021January 24, 2021

Baby Rudin: Let Me Help You Understand It!

The First in a Series of Blog Posts on Baby Rudin

Study Help for Baby Rudin, Part 1.1

Bill Kinney's personal copy of Baby Rudin (Principles of Mathematical Analysis, 3rd edition) — My personal copy of Baby Rudin (Principles of Mathematical Analysis, 3rd edition, by Walter Rudin)

The textbook “Principles of Mathematical Analysis”, by Walter Rudin, is considered a “classic” text on real analysis, the subject that uses rigorous deductive

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