Re: What can be said about e?


This reminds me of another question: Is there any obvious reason why
exp(x) should be equal to e^x for some number e? For example, why does
the above definition happen to satisfy the relationships we would
expect for powers, such as exp(a)*exp(b) = exp(a+b), exp(a)^b =
exp(a*b) etc. Sure you can show these relationships by applying brute
force to the series definition, but I'm talking about something much
simpler - something that follows in an intuitively clear way from some
definition of exp.

The identities follow from the DE: exp(x) is the unique solution to
y'=y, y(0)=1.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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