#e = 1+ 1/1 + 1/(2*1) + 1/(3*2*1) + 1/(4*3*2*1) + 1/(5!)+ 1/(6!) + * * *#

(For positive integer #n#, we define: #n! = n(n-1)(n-2) * * * (3)(2)(1)# and #0! = 1#

#e# is the coordinate on the #x#-axis where the area under #y=1/x# and above the axis, from #1# to #e# is #1#

#e = lim_(m rarr oo) (1+1/m)^m#

#e ~~ 2.71828# it is an irrational number, so its decimal expansion neither terminates nor goes into a cycle.

(It is also transcendental which, among other things, means it cannot be written using finitely many algebraic operations

(#xx, -: , +, -, "exponents and roots"#) and whole numbers.)