It is the limit approached by (1+1n)n as n increases without bound.
It is the limit approached by (1+n)1n as n approaches 0 from the right.
It is he number that the sum:
1+11+12+13⋅2+14⋅3⋅2+15⋅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)=ex.
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=1x 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=1x, then e is the number whose ln is 1.
