Why should we study real analysis? Once you are inside the first course of this beautiful subject, you will find hundreds of complicated theorems and formulas floating around the canvas. What makes this journey into rigorous deductive reasoning interesting is: we get to invent new numbers and functions!
Euler Number is one example. But it is just one of the infinitely many other numbers that were invented using tools of real analysis.
The story begins with an age old formula from bankers: