Discover the Transcendental Nature of E+pi at AMS Meetings

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SUMMARY

The discussion centers on the proof that e + π is irrational, rather than transcendental, as presented in a preprint from the AMS meetings. Participants engage with quizzes about the existence of irrational numbers that can combine with e and π to yield rational results. The conversation references a previous thread initiated by JF, highlighting the complexity of the topic and the need for more rigorous proofs. A link to a developing paper on arXiv is provided for further exploration.

PREREQUISITES
  • Understanding of irrational and transcendental numbers
  • Familiarity with mathematical proofs and their rigor
  • Basic knowledge of Lebesgue measure
  • Experience with mathematical discussions in English
NEXT STEPS
  • Read the AMS meeting paper on e + π for foundational insights
  • Explore the arXiv paper titled "0907.0467v4" for advanced proof techniques
  • Investigate the properties of Lebesgue measure in relation to irrational numbers
  • Review previous discussions on irrational sums in mathematics forums
USEFUL FOR

Mathematicians, students of number theory, and anyone interested in the properties of irrational and transcendental numbers will benefit from this discussion.

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thanks so much! I am fascinated by these problems! This is proving e+pi irrational, not transcendental.
 
Quiz:

Is there an irrational number x such that pi+e+x = (a rational number)?
 
Three and a half years ago JF started the same thread:

https://www.physicsforums.com/showthread.php?t=203040 .

Personally, I don't understand anything what that guy is saying. His mastery of the English language is also kind of off-putting.
 
Last edited by a moderator:
Antiphon said:
Quiz:

Is there an irrational number x such that pi+e+x = (a rational number)?

There are an infinite number of them and they are dense in R. They do have a Lebesgue measure of 0, though :biggrin:
 
Antiphon said:
Quiz:

Is there an irrational number x such that pi+e+x = (a rational number)?

i vote for r - e - pi, where r is rational.
 
Deveno said:
i vote for r - e - pi, where r is rational.

You win the quiz.
 
camilus said:
thanks so much! I am fascinated by these problems! This is proving e+pi irrational, not transcendental.
It agree I'm sorry:confused:
 
its okay. I don't understand the proof anyways, is there a more rigorous version somewhere else? this looks like a preprint or an outline, not the actual proof.
 
  • #10
camilus said:
its okay. I don't understand the proof anyways, is there a more rigorous version somewhere else? this looks like a preprint or an outline, not the actual proof.

http://arxiv.com/abs/0907.0467v4
This paper is under development, thank you for your patience while we expand it! o:)
 

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