Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Why the Epsilon-Delta Definition of Continuity Makes Sense

Audience:

Tags: continuity

I have attempted to help the reader discover how the epsilon-delta definition of continuity arises naturally. This article is intended to bridge the gap between intuition and rigour about the idea of continuity. When I first encountered this definition, I was encouraged to generalise it further, as much as I can. I quite enjoyed that feeling, and so I have attempted to give the reader a taste of the same feeling with this article. This article assumes familiarity with functions and is aimed at advanced high school/early undergraduate students.


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5.67 Overall score*
38 Rank
10 Votes
2 Comments

Comments

6.5

The idea of drawing graphs and lifting the pen is a beautifully simple way to introduce the idea of continuity using an analogy that anyone can understand. This article takes that one step further, though, by allowing the reader to actually play with that idea themselves through interactive graphs. This article is exceptionally well produced; the interactive elements are seamlessly integrated and provide a lot of value in understanding for a topic like this, which can be represented so physically.

5

Hey, nice job! I think that letting the idea of “single-stroke graphs” drive things is a good choice, and I think that does lead to a pretty fresh way to talk about this topic. I will say, I think the amount of notation you have in your article is likely to be a little intimidating for some of your target audience, and I think the build-up into the ideas of the delta-epsilon proof could’ve been a little softer - I think this might read better for me as someone who understands the concept already than it would for someone who needs help with the concept. But it represents an interesting way to communicate those ideas, it was an interesting read, and I hope you keep it up