Epsilon in Modern Use

Epsilon is one of several Greek letters that entered permanent mathematical use only through 19th-century calculus, long after the letter's ancient religious and numerical roots discussed elsewhere in this atlas were fixed. Augustin-Louis Cauchy and, later, Karl Weierstrass formalised the modern definition of a mathematical limit using epsilon to represent an arbitrarily small positive quantity, paired with delta to represent a correspondingly small change in an input variable, a convention now taught to virtually every student of calculus as the epsilon-delta definition.

By extension, mathematicians and scientists more informally use epsilon on its own to mean a negligibly small amount of anything, as in the phrase within epsilon of a value. Because ancient Greek used epsilon for a plain short vowel sound with no special weight, unlike the mother letters and long-vowel letters that carried extra classical significance, its selection for this modern technical role appears to reflect only its position early in the alphabet and its availability as an unclaimed symbol, rather than any inherited meaning; astronomers, following the Bayer star-naming convention of 1603, also use Epsilon to mark a constellation's fifth-brightest star.