Why is 2.71828182846...etc special? Is there any reason why e should equal 2.71828182846 and not some other number? I read that e is "transcendental" (what the hell does that mean- some kind of hippie spiritualism thing?). There must be some reason for why e=2.71828182846.(adsbygoogle = window.adsbygoogle || []).push({});

i know that the function e^x=y is special in that y=y'. (which after reasoning through it i realize that there must be such a number, because for 2^x=y, y>y' for all x values, and for 3^x=y, y<y' for all x values, so there should be a number between 2 and 3 such that y=y')

But how is e=(1+1/∞)^∞? (i dont know how to use that latex thing for limit notation, but you get the idea. actually i kind of prefer this definition over the definition that uses limit notation)

Some interesting things i discovered while playing with my calculator and want to know why:

(1+1/∞)^-∞=e^-1 (which makes sense- no questions here.)

(1-1/∞)^∞=e^-1 (that's really, really weird. why is this?)

(1-1/∞)^-∞=e (apparently the negatives cancel out somehow, but why? subtraction and inverse exponentation are two completely different things!)

Some other questions about e:

Why is e = ∑(1/n!) where n goes from zero to infinity?

And why does e^x= ∑(x^n/n!) where n goes from zero to infinity?

Why does the natural logarithm function work when finding the derivative of a^x? I always think of the logarithm as just a way to solve for x in the situation a^x=y

Are there any other weird things about e that i should know?

Also, a kind of unrelated thing, why does 0!=1?

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# Why is the number e special?

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