what is the purpose of the value e?
In: Mathematics
The ‘value’ e itself not nearly as interesting as the exponential function associated with that number, which happens to be the ‘most natural’ exponential form. This exponential function has some incredible properties which, along with some other fundamental assumptions, essentially lay the entire foundation for a significant chunk of modern mathematics. At face value, this function connects addition with multiplication, allowing efficient interchanging of the two operations which itself has tons of obvious applications. In fact, it goes deeper than that because the exponential function and its basic properties can be used to derive all of the fundamental relations involving, i.e. to define, the functions sine, cosine, etc… and essentially everything involving complex numbers has intimately to do with the connection between the exponential and trigonometric functions. I’m not a mathematical expert, but I know enough to recognize that the function is of tremendous importance, probably to a degree we don’t even fully comprehend yet.
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