The Archimedean Property

The Completeness Axiom is a sufficient condition to prove the Archimedean Property, but is it necessary?

Real Analysis Study Help for Baby Rudin, Part 1.5

*A Visualization of the Archimedean Property in the case where $x=8$ and $y=70$ . The smallest positive integer value of $n$ that makes $nx>y$ is $n=9$ .*

*A Visualization of the Archimedean Property in the case where $x=8$ and $y=70$ . The smallest positive integer value of $n$ that makes $nx>y$ is $n=9$ .*

Does the sequence $\left(\frac{1}{n}\right)_{n=1}^{\infty}$ approach zero as $n\rightarrow \infty$ ? Sure! After all, given any number

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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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January 22, 2019July 18, 2019

Deconstructing the Mean Value Theorem, Part 3

The Mean Value Theorem implies that there is at least one tangent line with the same slope as the secant line.

Pete Brady strolled out of the U.S. Postal Service office just off Weaver Lake Road in Maple Grove, Minnesota at exactly 10 am.

Coffee and important package in hand, he set off on his 161 mile (259 kilometer) journey … Read the rest

January 3, 2019March 4, 2019

The Road Ahead

My plans for this blog are ambitious.

My main goal for Infinity is Really Big is to bring you excellence in mathematical content for your personal and professional growth.

YouTube-Related Content

As of the early January 2019, my YouTube channel, “Bill Kinney Math“, is moderately successful. It has over half a million views and over 4400 subscribers. The … Read the rest