Mark has 60+ answers in. Mathematics. Epsilon is just a Greek letter that's used by mathematicians when they've run out of Roman letters. Normally only the lower-case version, [math]\epsilon[/math], is used, because the upper-case version is not distinctive: E. Probably the most famous use is in the so-called epsilon-delta definition of a limit (see (ε, δ)-definition of limit). Roughly, a function f(x) has the limit l as x approaches a if, for any small range delta, you can make f(x) be closer than delta to l by picking x within epsilon of a. So epsilon is sometimes used as a metaphor for a very small error range around a point.