existence of roots Archives - Infinity is Really Big

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

… Read the rest

January 14, 2020January 14, 2020

Applied vs Pure Mathematics

Calculus 2, Lecture 1 (Videotaped Fall 2016)

Population modeling is an important part of applied mathematics in calculus. It is a good example to start with in looking at the nature of applied vs pure mathematics. — Population modeling is an important part of applied mathematics in calculus.

Calculus is at the heart of much of modern mathematics and its applications. Its discovery by Newton and Leibniz sparked the scientific revolution and enlightenment of the 1600’s and 1700’s and brought about our modern world.

Throughout mathematical history, … Read the rest