# How can ∈ be less than/ greater than something?

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

• Seems to be a lower case epsilon. – Will Jagy Sep 21 '18 at 23:40
• 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 $\epsilon$ – Will Jagy Sep 21 '18 at 23:42
• @Will Jaggy quite possibly – Max0815 Sep 21 '18 at 23:47
• 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). – Asaf Karagila Sep 22 '18 at 0:19
• 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. – Robert Israel Sep 22 '18 at 1:15

"$$\in$$" 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.