This means (from atomist quantum) point of view that e is time (or alternatively space) dependent \(2\ge e <= \lim_{n\to\infty} (1 + 1/n)^{n}\).One glaring omission is that no one has mentioned how [$]e[$] came to be. Everyone blames Euler (some blame APL) but its roots are probably due to a 17th century banker or trader who stumbled oncompound interest:

[$]\displaystyle\lim_{n\to\infty} (1 + r/n)^{nt} \rightarrow e^{rt}[$]

Then the special case gives us

[$]\displaystyle\lim_{n\to\infty} (1 + 1/n)^{n} == e[$]

e for one second is [$] (1 + \frac{1}{\frac{c}{l_p}})^{\frac{c}{l_p}} =(1 + \frac{l_p}{c})^{\frac{c}{l_p}} == \mbox{True } e \approx (1 +5.39106\times 10^{-44}

)^{1.85492\times10^{43}} \approx \lim_{n\to\infty} (1 + r/n)^{n}\approx 2.718281828

[$]

e for one Planck second must be [$] (1 + 1/n)^{n}= (1 + 1)^{1} == 2 [$] (me-2)

True \(e^5==2^5==32\) for one Planck second.

(PS The limit of n is 1 inside one Planck second and inside one Planck mass particle, the turning point of light.

everything else is opinions, bad smelling onions and approximations

Dont worry your approximation methods will work very well until we are closing in on the Planck scale.

"How to compute \(e^5\) with two decimal places?" ==32.00 ($ or kr your choice)

or are u guys working on the elementary charge? sorry I just discovered this thread, is it new? Skål!