 # "Why is e so special? The number e (and the exponentiation function ex) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why. " frobirrimupyx 2022-09-14 Answered
Why is e so special?
The number e (and the exponentiation function ${e}^{x}$) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why.
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Because very many of humanity's age-old mathematical interests ultimately converged towards it:
Arithmetic:
Addition begets multiplication; multiplication begets exponentiation; exponentiation begets e, seeing that by using reading it we inevitably arrive at the conclusion that this number is its most herbal base.
tends to e as n tends towards infinity.
Geometry:
Circles and hyperbolas have been studied since ancient times; e is to the latter what $\pi$ is to the former.Finance:
Examining the way in which banking interests are computed leads us to discovering the same quantity.Calculus:
The harmonic series has been studied since ancient times; its continuous equivalent is $={\mathrm{log}}_{e}x$
The solution to $f\left(x\right)={f}^{\prime }\left(x\right)$ is , meaning that the exponential function is immune to the operations of differentiation and integration.

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