# Post by Give: e

e…

d

c

=mc^2

b

a

2.718281828 . . .

Is a transcendental thing…

One of the best threads we have had in the investments section for a while IMO…

Pi^e vs e^Pi - which is larger? No calculators or spreadsheets. Go!

Is there such a thing as a negative e? Like an imaginary e?

There is -e.

There is also imaginary e, which is simply i*e

More interestingly, e^(ix) produces a sine wave (technically a cosine wave) along the real axis in the complex plane (and a sine wave along the imaginary axis).

There’s also silent e:

e^pi is larger isn’t it? I remember doing the proof of that years ago

I don’t know how to prove it analytically, but according to my R console:

e^pi ~ 23.14069…

pi^e ~ 22.45916…

(e^pi - pi^e) ~ 0.6815349…

That’s a big enough difference that one should be able to judge it by doing a calculation with a long enough approximation.

My guess is that the proof could be accomplished by comparing Taylor series expansions for each, subtracting one from the other, and then showing that for any delta, the difference is always positive or negative, depending on the order of subtraction.

We did the proof using natural log to cancel shit out and somewhow ended up at the right answer

that is indeed the right approach

The right approach is to use naturally-occuring logs to shit out when deciding which is greater–e to the pi, or pi to the e.

Good to know.

You’ve always seemed to be one of the few technical posters on here. What type of work are you in?

That’s exactly what the OP had in mind when he started this thread.

I’ll bet there is a product being marketed for people with Low E.