It is the limit approached by (1+1/n)^n as n increases without bound.
It is the limit approached by (1+n)^1/n as n approaches 0 from the right.
It is he number that the sum:
1+1/1+1/2+1/(3*2)+1/(4*3*2) + 1/(5*4*3*2) + . . . approaches as the number of terms increases without bound.
It is the base of the function with y intercept 1, whose tangent line at (x, f(x)) has slope f(x). This function turns out to be the exponential function f(x) = e^x.
It is the base for the growth function whose rate of growth at time t is equal to the amount present at time t.
It is the value of a for which the area under the graph of y=1/x and above the x-axis from 1 to x equals 1.
If we define lnx for x>+1 (as we often do in Calculus 1) as the area from 1 to x under the graph of y=1/x, then e is the number whose ln is 1.
