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The limit of the expression as tends to infinity:

it is the base for the natural logarithm. is a transcendental number, which was proved by C. Hermite in 1873 for the first time. Sometimes is called the Napier number for no very good reason.


See also Exponential function; Exponential function, real; Logarithm of a number; Logarithmic function; Transcendental number.

How to Cite This Entry:
E-number. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article