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 June 14th, 2012, 11:52 AM #1 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Limit and Transcendence If $\phi$ is an transcendental number, then phi is always expressible by limits or in other words, $\phi= \lim_{x \rightarrow a} f(x)$ Is it true? I know it is true for some of my known non algebraic numer like ? and e, and cannot find a contradiction. Just curious nothing more Note to moderators: I accedentally posted this topic on number theory, I request to the moderators for moving this topic to intruduce yourself and other topics because it is an off-topic discussion about number theory.
June 14th, 2012, 01:30 PM   #2
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Re: Limit and Transcendence

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 Originally Posted by mathbalarka If $\phi$ is an transcendental number, then phi is always expressible by limits or in other words, $\phi= \lim_{x \rightarrow a} f(x)$ Is it true?
It's true for any number, transcendental or algebraic, in uncountably many ways. For example, pi is the limit of the function f(x) = pi as x increases without bound, and of the function g(x) = pi + 1/x as x increases without bound, and of the function h(x) = 3 if x < 7 and pi * x/(x - 1) otherwise, and ....

June 14th, 2012, 01:32 PM   #3
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Re: Limit and Transcendence

Quote:
 Originally Posted by mathbalarka Note to moderators: I accedentally posted this topic on number theory, I request to the moderators for moving this topic to intruduce yourself and other topics because it is an off-topic discussion about number theory.
I moved it to "Applied Mathematics, Set Theory, Logics and other", which is where math topics that don't fit elsewhere go. Introductions & other is for nonmathematical topics which don't belong elsewhere.

June 14th, 2012, 01:43 PM   #4
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Re: Limit and Transcendence

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Originally Posted by CRGreathouse
Quote:
 Originally Posted by mathbalarka Note to moderators: I accedentally posted this topic on number theory, I request to the moderators for moving this topic to intruduce yourself and other topics because it is an off-topic discussion about number theory.
I moved it to "Applied Mathematics, Set Theory, Logics and other", which is where math topics that don't fit elsewhere go. Introductions & other is for nonmathematical topics which don't belong elsewhere.
Thank you.
Well, there are some mathematical topic which is in Introduction and other: An interesting fraction
Anyways, thank you!

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