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June 14th, 2012, 11:52 AM   #1
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Limit and Transcendence

If is an transcendental number, then phi is always expressible by limits or in other words,

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.
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June 14th, 2012, 01:30 PM   #2
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Re: Limit and Transcendence

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Originally Posted by mathbalarka
If is an transcendental number, then phi is always expressible by limits or in other words,

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

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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.
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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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