Euler's number (idea)
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Actually something a little more general is done . The WU below tries to explain how xr is defined when r is real. Note that for rational and integral r we have no problem. When r is irrational the situation becomes a little problematic. So this is what we do.
We then show that this power series expansion satisfies common properties of exponentials such as exp(a+b)=exp(a)*exp(b) etc. After this we define an inverse to the exponential function and call this inverse log(x). Finally we define