This is based on Bernoulli's compound interest definition.
But let's say we want to find $e^x$ now.
Let $m = nx$ so $n = m/x$. As $n$ goes to infinity, so does $m$, so:
This now looks like the definition you usually see but apparently this is an invalid proof of the fact because $n$ is supposed to be an integer(??) and $m/x$ may not be.
How are you supposed to get from one to the other then?