Does e Have a Meaning?
Does e mean anything? Or is it just an artifact—a number that’s just a result of the way that numbers work?
That’s more a question for philosophers than mathematicians. But I’m inclined to say that the number e is an artifact, but that the natural logarithm is deeply meaningful. The natural logarithm is full of amazing properties: it’s the only logarithm that can be written with a closed-form series; it’s got that wonderful interval property with the 1/x curve; it really is a deeply natural thing that expresses very important properties of the basic concepts of numbers. As a logarithm, the natural logarithm had to have some number as its base; it just happens that it works out to be the value e. But it’s the logarithm ...
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