My Math Forum Limit and Transcendence
 User Name Remember Me? Password

 Applied Math Applied Math Forum

 June 14th, 2012, 10:52 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, 12:30 PM   #2
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Limit and Transcendence

Quote:
 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, 12:32 PM   #3
Global Moderator

Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
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, 12:43 PM   #4
Math Team

Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Limit and Transcendence

Quote:
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!

 Tags limit, transcendence

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mathbalarka Number Theory 23 May 9th, 2013 05:28 AM czar01 Applied Math 4 November 22nd, 2012 01:16 PM mathbalarka Calculus 0 September 3rd, 2012 07:02 AM conjecture Calculus 1 July 24th, 2008 01:14 PM mathbalarka Number Theory 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top