What is oilers number?

Answer 1

You are referring to Euler's number. It is pronounced like "eh-uh-le-uh" because the name is German. Euler's number is the number e, which is the base of the natural logarithm. The number e is extremely prominent in any mathematical endeavour involving calculus in any way, as it has many useful properties. For example, the derivative of the function f(x) = e^x is the function df(x) = e^x = f(x). It is the only function that has this property.

The natural logarithm is itself also very useful. It was discovered by studying properties of the integral of the function f(x) = 1/x, which did not have any closed form antiderivative in terms of the elementary functions of that time period, even though g(x) = x^n had the simple antiderivative Ig(x, C) = (x^(n+1))/(n+1) + C for any real n except n = -1.

It was eventually discovered that the function f(x) defined as the definite integral of f(t) = 1/t from t = 1 to t=x had the properties of a logarithmic function with base e. e is transcendental, so it is both irrational and is not the root of any polynomial function with rational coefficients. Or in simple words 2.718281828459