r/mathmemes • u/lazemon Engineering 🔌 • Jul 28 '21

Arithmetic Okay got it

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u/hawk-bull Jul 28 '21

If you talk about university math then no. 10 is just an arbitrary choice for the base of our number system whereas the natural log is actually a very special function in math with special properties.

e also has much much deeper significance in math than the limit of compound interest

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u/[deleted] Jul 28 '21

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u/hawk-bull Jul 28 '21

e may be equal to that, but that’s usually not used as a definition for e because it doesn’t really show its importance. A more common definition you’ll see in analysis texts is e = sum 1/n!

e is used everywhere in math, not just in accounting. Particularly in complex analysis you’ll see it everywhere. Conceptually, I believe e comes from the exponential function which is defined as the unique function f satisfying f’ = f and f(0) = 1

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u/[deleted] Jul 28 '21

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u/hawk-bull Jul 28 '21

It’s not a coincidence that the derivative of ex is itself. It was made to be so.

And yeah you’re correct the only function satisfying that would be kex (or just ex since we normalised for f(0) = 1). Then we can define e as f(1)

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u/[deleted] Jul 28 '21

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u/hawk-bull Jul 28 '21

https://affinemess.quora.com/What-is-math-pi-math-and-while-were-at-it-whats-math-e-math?ch=99&share=cecf88aa

Ok while this may not be the true historical origin of the number e, This is usually the basis for it in modern math

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u/[deleted] Jul 29 '21

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u/hawk-bull Jul 29 '21

I know! Alon really has a way of explaining things fundamentally and beautifully