The Foundations of a Non-Naive Mathematics

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The discussion centers on a new mathematical framework proposed by Lama, which aims to redefine fundamental concepts such as tautology, sets, and the real line. Key axioms include the independence of points and segments, the duality of elements, and the completeness of collections. The framework emphasizes the relationship between absolute and relative properties, suggesting that the real line is a fractal system with invariant cardinality across various scales. Critics question the validity of the proposed definitions and their equivalence to established mathematical constructs like Dedekind cuts and Cauchy sequences. The conversation highlights a clash between traditional mathematics and Lama's innovative approach, which seeks to address complexities overlooked by conventional methods.
  • #511
So ex-xian and kaiser soze,

If you still cannot understand by reading my work that I cannot write what I write without a deep understanding of standard reasoning, then you have no ability to see beyond what you learned in your school of thought.
 
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  • #512
Lama said:
So ex-xian and kaiser soze,

If you still cannot understand by reading my work that I cannot write what I write without a deep understanding of standard reasoning, then you have no ability to see beyond what you learned in your school of thought.
Prove that you have this understanding. You offered to before! Here, I'll quote you again.
Lama said:
Please demonstrate some fundamental mathematical idea, which can clearly show that I do not understand (again, not disagree with, but do not understand) its standard interpretation.
If you don't, you've just lost what little credibility you might have retained.
 
  • #513
Ex-xian,

Do you know what is a fundamental Mathematical Idea (and I do not mean to some basic techniques to prove things)?
 
Last edited:
  • #514
Do the problems, which you asked for, or admit that you can't. It's as simple as that.

A correction: the operation for the abelian group problem should have been circle addition, not addition. Addition isn't an operation for Zmodn.
 
  • #515
It seems that for every single question that is asked of Lama, he either cuts and pastes old posts or posts a link to his book. This has gone on for 26 pages, and there is no indication that it will not go on for another 26, if left on its own. Since there is no need to waste bandwidth at PF on that sort of back-and-forthing, I'm putting a stop to it now.

Here's that link again: http://www.geocities.com/complementarytheory/No-Naive-Math.pdf

Apart from that, say goodnight to this thread.
 

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