List: The Limit Series | Curated by Joseph Mellor | Medium

Jul 26, 2021

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The Limit Series

In this series, I establish what a limit is, explain the two main types of convergence, and then prove the Moore-Osgood Theorem, which specifies when you can switch limits in calculus.

In

Cantor’s Paradise

by

Joseph Mellor

Let’s Derive the Power Rule from Scratch!

From nothing but the definitions of derivatives and exponentiation, we’ll prove one of the first derivative rules you’ll learn in college

Aug 17, 2020

Let’s Derive the Power Rule from Scratch!

Aug 17, 2020

In

Cantor’s Paradise

by

Joseph Mellor

What is a Limit, Really?

You’ve seen limits in Calculus class and you know it has something to do with approaching, but how would you use it in a proof?

Jul 10, 2021

What is a Limit, Really?

Jul 10, 2021

In

Cantor’s Paradise

by

Joseph Mellor

Uniform and Pointwise Convergence

How can a sequence of continuous functions converge to a discontinuous function?

Jul 18, 2021

A bridge with the cables converging in the center of the image.

Jul 18, 2021

In

Cantor’s Paradise

by

Joseph Mellor

When Can You Switch Limits in Calculus?

Buckle up. Real analysis pulls no punches.

Jul 22, 2021

limit as x approaches a limit as y approaches b of f of x and y equals with a question mark limit as y approaches b limit as x approaches a of f of x and y equals with a question mark limit as (x, y) approaches (a, b) of f of x and y. Basically, does switching the order of limits or taking both at the same time affect the output?

Jul 22, 2021

Joseph Mellor

Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at https://josephmellor.xyz/articles/.

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