Augustin-Louis Cauchy in 1821, followed by Karl Weierstrass, formalized the definition of the limit of a function which became known as the (ε, δ)-definition of limit. The definition uses ε (the lowercase Greek letter epsilon) to represent any small positive number, so that "f(x) becomes arbitrarily close to L" means that f(x) eventually lies in the interval (L − ε, L + ε), which can also be written using the absolute value sign as |f(x) − L| < ε
