What Is Epsilon in Math?

Epsilon in math, represented by the Greek letter “E,” is a positive infinitesimal quantity. Essentially, it denotes a very small number that is not negative, approaching zero but staying positive.

The epsilon is used in the epsilon-delta definition of the limit. This notation is the formal representation of forming the limit of a function at a specific point. Sometimes called the precise definition, it is written out as lim F(X) = L as X approaches A. This equation notates how close to L the F(X) should be. This closeness is somewhat arbitrary, but if the “lim F(X)” side of the equation is less than the epsilon, it stays within the limits of the epsilon.

Scientist and physicist Sir Isaac Newton worked with these concepts and referred to them in his work. He wrote of ratios that were not ratios with set quantities, but rather limits that they approached so closely that the difference was negligible.

Mathematician Augustin-Louis Cauchy began developing this idea by using arguments based on delta and epsilon in his proofs. He called this concept “variable quantities.” Nobody provided the formal definition until Bernard Bolzano first notated this limit in 1817. Its definitive modern version was provided by Karl Weierstrass.