Do you know any number that cannot be written as a simple fraction? Most of you will say, “π”.
π is an irrational number, as I told you last time, and is also important in our life. Is there another important irrational number that is used in our life? Many people won’t know, but everyone should have to know this: irrational numbers like are common. It is called Euler’s number,e , which is originated from a mathematician named Leonard Euler; however, he was not the one who found e. There was another mathematician before Euler who found limit as x approaches of (1+1/x)^x equals 2.718182818…….
e is used in mathematics, physics, and even in economics. Numerically, e is approximately 2.718. The exponential function e^x is a special function. Why? The derivative of e^x is the same as the original function.
Is e possible to approximate with fractions? Unfortunately it is not;however it is the addition of infinite amount of fractions.
Here is the proof.