Also, while the limit that LifeWillFall can be used as a definition, it’s not.
I learned “e” rather torturously. First, demonstrate that the indefinite integral of 1/x from 1 to (whatever) has all the rules of a logarithm. Define exp(x) and the inverse of the integral function. Do other messing around with it and find the incredible power of the number e. We spent a long time messing with the natural log and the natural exponential function in my calc class. I loved every stinkin’ minute of it.
Achernar, your proof is the same as his. I don’t really understand how it works, maybe its beyond me at the present moment…