as x goes to infinity, ((1+(1/x))^x), that's all i know
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My improvement to the previous answer is to then try to explain why it is then called "natural". The initial formula shown above, even though it is 100% right, is not the origin of itself and some further explanation of it may then be needed.
e is sometimes called "Euler's Number" Euler was a mathematician who
conceived of this value.
e or epsilon is a constant value of about 2.71828 e is a very important number like PI = 3.14...
This is called a natural number because it occurs in nature alot like the Fibonacci series or numbers. e was chosen since it can then be used to calculate natural growths and decays. For example an object that is cooling down, the temperature can be calculated where the formula for that has e in it. A series for e has been developed which has great power in finding not only powers of e but powers and roots of any value since series for those values have not been developed (such as a series for powers of 10).
The definition of e is based upon (1/1 + 1/n)^n where n is very high. Quickly though it reaches 2.718 even when n is lower. The value of this expression approaches the value of a constant we will just call e. If you have infinitely compounded growth during one period of time, the initial value will grow to about 2.718 times bigger for that entire period, and not some enormous value like some might think initially. The reason is that the compounded growth value to be added in gets very small when the number of intervals (n in the formula) of compounded growth is very high.
Read more: What is the natural base of e
the natural number Euler's number
The number e, 2.718281828..., was chosen as the "natural" base for logarithms and powers because it is the only number where the deriviative of e to the x is x... d/dy ex = x
It is Euler's number which is the base of natural logarithms.
The number is called e, and it is approximately equal to 2.718.
The natural logarithm is calculated to base e, where e is Euler's constant. For any number, x loge(x) = log10(x)/log10(e)