The Number e
The constant 
is base of the natural logarithm. 
is sometimes known as Napier's constant, although its symbol (
) honors Euler.
is the unique number with the property that the area of the region bounded by the hyperbola 
, the x-axis, and the vertical lines 
and 
is 1. In other words, |
, 
is the most important constant in mathematics since it appears in myriad mathematical contexts involving limits and derivatives. The numerical value of 
is |
can be defined by the limit |
 |
is given by the unusual limit
|