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How can ∈ be less than/ greater than something? Specifically in the equation |a∗a−x| ≤ ∈. From my understanding ∈ means 'is an element of" and used like this: 'Let a∈A' means 'Let a be an element of A'. How can it be less than/ greater than something? Thanks

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    $\begingroup$ Seems to be a lower case epsilon. $\endgroup$ – Will Jagy Sep 21 '18 at 23:40
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    $\begingroup$ where was I: in Latex, set membership is $\in$ while the two main versions of epsilon are $\epsilon$ and $\varepsilon$ It would appear that you or someone printing mixed up $\in$ and $\epsilon$ $\endgroup$ – Will Jagy Sep 21 '18 at 23:42
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    $\begingroup$ @Will Jaggy quite possibly $\endgroup$ – Max0815 Sep 21 '18 at 23:47
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    $\begingroup$ Not to mention that $\in$ was denoted by $\varepsilon$ in some older texts, and is still sometimes referred to as "epsilon relation" (e.g. $\in$-induction is called "epsilon-induction" sometimes). $\endgroup$ – Asaf Karagila Sep 22 '18 at 0:19
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    $\begingroup$ It's a matter of typography. Peano used an "uncial" $\epsilon$. I don't know how this morphed into the stylized $\in$, or how readily available the latter would be in the days before TeX. $\endgroup$ – Robert Israel Sep 22 '18 at 1:15
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There are two similar-looking but different-meaning symbols.

"$\in$" is used for "element of a set".

"$\epsilon$" (Greek letter epsilon) is used for a number or variable (in your case, probably a positive Real number).

"$\varepsilon$" is another form of epsilon.

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