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I'm going through the limits in the book and here is one of the exercises:

Find an open interval about $c$ on which the inequality $|f(x) - L| < \epsilon$ holds:

$f(x) = mx, m > 0, L=2m, c=3, $ $\epsilon = c > 0$

Usually in these exercises $\epsilon$ would be a number, but now it's an expression. And I don't understand how to read it.

Does it mean $\epsilon$ equals $c$ if $c >0$?

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Stanislav Bashkyrtsev
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1 Answers1

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It means that $\epsilon=c$ and $c>0$ (and consequently $\epsilon>0$ as desired. Incidentally, $c$ itself is given by a fixed value, $c=3$. So you may convert this to read $\epsilon=3>0$, read "$\epsilon$ is the number $3$, which is positive".

Hagen von Eitzen
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