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The number $e = 2.718281828...$ is the base of the natural logarithm. Its decimal representation is infinitely long.

Why does this mathematical constant contain an infinite number? What is the reason behind this?

added for clearance: it contains infinitely long numbers, which does not repeat itself, how is this proven? it should at some point has some repeated numbers.

can it be represented by a fraction? ex: 1/2?

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    What do you mean when you say it contains an infinite number? And, BTW, the expansion for $e$ is _not_ periodic.2011-09-11
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    http://en.wikipedia.org/wiki/Proof_that_e_is_irrational2011-09-11
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    You mean, why did anybody define such a number in the first place? Because "it's irrational" **is** the reason why it has an infinite non-repeating decimal expansion.2011-09-11
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    The "part to the *left* of the decimal point" is obviously always only finitely long. You mean to the right of the decimal point. And, by the way, do you know that the decimal expansion of $1/3$ is $0.333\ldots$, with a string of infinitely many 3's following the decimal point?2011-09-11
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    sorry for the question guys, but i edited it now, so it is much clearer what im trying to say.2011-09-11
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    It isn't clearer to me. What do you mean when you say that $e$ contains an infinite number? If all you mean is that $e$ is not a terminating decimal, well, that's implied by the irrationality of $e$, and you've been given a reference to a proof of that. What do you mean when you say $e$ should have some repeated numbers? Of course it has some repeated digits, just look at all those 8s, but it isn't periodic, it isn't what's called a repeating decimal; again, that's implied by its irrationality. So I don't see what you are asking that hasn't already been answered.2011-09-11
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    It is (probably) true that every finite sequence of digits not only appears in the decimal expansion of $e$, but is appears infinitely often (see the "normal number" link you got in the answers). But when mathematicians say "repeating decimal", what they mean is that the decimal representation ends in a certain pattern -- a particular sequence of digits that keeps repeating, with nothing else appearing in-between the copies. Do the answers answer your question? From your edit, I think they do.2011-09-11

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