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We know, for example, the constant $\pi$ is the perimeter of a circle with diameter $1$ unit. In the similar manner how would we explain the constant $e$. I have searched a lot for it. But I couldn't comprehend it in a practical way. Can anybody help me to understand the constant $e$?

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marked as duplicate by AWertheim, Bruno Joyal, nbubis, T. Bongers, Bill Cook Nov 6 '13 at 4:52

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$ e^x $ is its own derivative, which makes it quite significant in calculus. –  The Chaz 2.0 Nov 6 '13 at 4:07
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betterexplained.com/articles/… –  cygorx Nov 6 '13 at 4:13
    
At 100% annual interest rate, compounded continuously, an initial deposit of \$1 will grow to \$e in one year. –  bof Nov 6 '13 at 4:54

1 Answer 1

For someone who hasn't taken calculus, understanding what $e$ is can be difficult. The reason is that the ways in which we define $e$ use calculus concepts. For example, we can define it as the sum of a certain infinite series, as the limit of a certain expression (see below), or we can give a derivative-based definition (which The Chaz 2.0 mentioned in his comment). There is no easy-to-picture geometric interpretation of $e$ like there is for $\pi$. But once you understand the calculus concepts we use to define $e$, you'll have a better understanding of what it is.

If you do know some calculus, perhaps easiest way to think of $e$ is as the limit $$e = \lim_{n \to \infty} \big(1 + \frac{1}{n}\big)^n$$

The examination of this limit is how $e$ was first discovered.

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