E

We define the real number $e$ to be the number such that $$\displaystyle\int_1^e \dfrac{1}{t} \mathrm{d}t=1.$$ By the definition of the logarithm, we have $\log(e)=1$. The value of $e$ is $$e=2.71828182846\ldots.$$

Properties

Euler's formula
e is irrational
Log e(z)=log(z)
Log 10(z)=log 10(e)log(z)

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.16$

Who proved $e$ is irrational?