- #1
Discover the Transcendental Nature of E+pi at AMS Meetings
- Context: Graduate
- Thread starter J.F.
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the nature of the sum of the mathematical constants e and π, specifically exploring whether e + π is irrational or transcendental. Participants engage with related problems and references, including quizzes about irrational numbers and previous discussions on the topic.
Discussion Character
- Exploratory
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants express fascination with the problems related to proving e + π irrational, rather than transcendental.
- A quiz is posed regarding the existence of an irrational number x such that π + e + x equals a rational number, with multiple responses suggesting various forms of x.
- One participant mentions a previous thread on the same topic, indicating a lack of understanding of the arguments presented in that discussion.
- Another participant questions the rigor of the proof provided, suggesting that it appears to be a preprint or outline rather than a complete proof.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on whether e + π is irrational or transcendental, and there are multiple competing views regarding the nature of the proofs and the related quizzes.
Contextual Notes
Some participants express confusion about the proofs and seek more rigorous versions, indicating limitations in the clarity and completeness of the materials discussed.
Who May Find This Useful
Readers interested in mathematical proofs, irrational numbers, and the properties of e and π may find this discussion relevant.
- #2
camilus
- 146
- 0
thanks so much! I am fascinated by these problems! This is proving e+pi irrational, not transcendental.
- #3
Antiphon
- 1,685
- 4
Quiz:
Is there an irrational number x such that pi+e+x = (a rational number)?
Is there an irrational number x such that pi+e+x = (a rational number)?
- #4
Landau
Science Advisor
- 905
- 0
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.
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.
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- #5
- 22,170
- 3,333
Antiphon said:
There are an infinite number of them and they are dense in R. They do have a Lebesgue measure of 0, though
- #6
Deveno
Science Advisor
Gold Member
MHB
- 2,726
- 6
Antiphon said:
i vote for r - e - pi, where r is rational.
- #7
Antiphon
- 1,685
- 4
Deveno said:
You win the quiz.
- #8
J.F.
- 34
- 0
It agree I'm sorrycamilus said:
- #9
camilus
- 146
- 0
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
J.F.
- 34
- 0
camilus said:
http://arxiv.com/abs/0907.0467v4
This paper is under development, thank you for your patience while we expand it!
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