Why exactly was $\epsilon$ chosen to denote a very small quantity?

Question

I tried to search the defintion of $\epsilon$, but only got that it is the fifth letter in the Greek alphabet.

I want to know why it was chosen the way it was?

This is something not very obvious, unlike the symbol $\in$, which means element of. That makes sense because $\in$ looks like an $E$ which can stand for element.

But epsilon is just an alphabet letter, and so why was it chosen?

I think that $\epsilon$ and $\delta$ were chosen because they're consecutive letters in the Greek alphabet. — Ben Grossmann, Jul 02 '17 at 23:31
@Omnomnomnom first of all, sickass name. Secondly, I agree they are, make I want to know why specifcally those? Was it random? I don't see an english linkage like how $\in$ has — K Split X, Jul 02 '17 at 23:32
I've always thought of $\epsilon$ as error and $\delta$ as a small change (like $\Delta x$). I can't speak for Weierstrass and Bolzano. — Ted Shifrin, Jul 02 '17 at 23:34
I think $\delta$ was chosen because it sounds like the "d" in difference. Also the upper case, $\Delta$ was being used to indicate a small change in a quantity. After that, $\epsilon$ was chosen because it is the next Greek letter after $\delta$. — Steven Alexis Gregory, Jul 02 '17 at 23:35
Possible duplicate of https://math.stackexchange.com/questions/530792/who-gave-you-the-epsilon — Dhruv Kohli, Jul 02 '17 at 23:45
@stevengregory I agree that's likely it, but do you have a source on the use of $\Delta$? — Chris, Jul 03 '17 at 00:08
I don't know, but I like to think of $\varepsilon$ as standing for error. — bof, Jul 03 '17 at 04:15
See the post: Who gave you the epsilon ?: Cauchy in his 1823 textbook used trhe Greek letters $\alpha, \beta, \gamma, \delta, \epsilon, \ldots$ for "nombres très-petites" (very small numbers). In the first chapter he started using $\alpha$ and $\beta$ and in the proof of the Theorem (7th Lecture) he introduced $\delta$ and $\epsilon$. Thus, I think that there is no special "allusion" behind the choice of them. — Mauro ALLEGRANZA, Jul 03 '17 at 06:17
https://mathoverflow.net/questions/82302/why-do-we-use-epsilon-and-delta — Hans Lundmark, Jul 03 '17 at 06:22
@amWhy... funny you say that given your name includes the word "Why" — K Split X, Jul 16 '17 at 01:50

Why exactly was $\epsilon$ chosen to denote a very small quantity?

0 Answers0