How can ∈ be less than/ greater than something?

Question

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

Answer 1

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.