Is the Real-Line a Fractal? Weak Points Examined

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Discussion Overview

The discussion centers around the question of whether the real line can be considered a fractal, exploring the implications of certain mathematical definitions and concepts. Participants examine the claims made regarding the nature of the real line, its members, and the idea of self-similarity across scales.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant proposes that if any local member of the real line can also act as a global scale factor, then the real line may be classified as a fractal.
  • Another participant challenges the initial claim by stating that it begins with a conditional statement and lacks proof of a non-vacuous case.
  • Concerns are raised about the clarity and definitions of terms such as "local," "member," "global," "scale," and "fractal," suggesting that these need further explanation.
  • A participant argues that the model presented allows any member of the real line to exist simultaneously as a unique number and as a global scale factor, emphasizing the self-similarity of the real line.
  • Another participant questions the terminology used, specifically the term "ultimative fractal," and expresses confusion over its meaning.
  • Critiques are made regarding the lack of definitions for key concepts like "global scale factor" and "magnitude," suggesting that the arguments presented are not sufficiently rigorous.
  • One participant asserts that the discussion has not adequately addressed the relationship between fractals and the infinite nature of the real line.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of the concepts discussed, with no consensus reached on whether the real line can be classified as a fractal. The discussion remains unresolved, with multiple competing interpretations of the claims made.

Contextual Notes

Participants note limitations in the definitions and clarity of terms used in the discussion, which may affect the understanding of the arguments presented. There is also a suggestion that the mathematical rigor expected in such discussions has not been met.

Shemesh
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Reexamination of the Real-Line

If any local R member is also a global scale factor on the entire real-line and this duality recursively defines R members, then the real-line is a fractal as I show here:

http://www.geocities.com/complementarytheory/Real-Line.pdf


Please show me what are the weak points here?

Matt Grime said:
1. you begin with an if for a start, and don't prove that it is a non-vacuous case, but that could be hard because:
2. none of those terms are extant, ie known, or if they are you are using them in a way that is not understood by anyone else

words that need explanation:
local, member (but we presume you mean element), global, scale, factor, duality, fractal (you would need to prove that this statement is equiavalent to the statement R is a fractal)
 
Last edited:
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An explanation of Vacuous Truth can be found here: http://en.wikipedia.org/wiki/Vacuously_true#Vacuous_truths_in_mathematics

If you look at http://www.geocities.com/complementarytheory/Real-Line.pdf , you can see that by this model any member (or element) of R set can be simultaneously in both states:

1) As some unique number of the real line (a unique member of R set)

2) As a global scale factor on the entire real-line, which its product is the entire real-line included in itself according to this global scale.

There is no process here but a simultaneous existence of R set on infinitely many unique scale levels of itself.

Because of this self-similarity over scales, we can understand why some segment of the real line can have the magnitude of the entire real-line.

Please understand that we are not talking about some shape of a fractal, but on the infinitely many levels of non-empty elements, which are included in R set.

It is important to stress that there is one and only one magnitude to the real line, which is not affected by its fractal nature.


Any comments?
 
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What is an "ultimative fractal" ?

No, wait, what is "ultimative" ? Or, is that German ?
 
1. You've not explained what global scale factor means, just used the words again.
2. if fractals have nothing to do with it why do you keep banging on about them
3. R is an infinite set, that is all youy're saying
4. magnitude has not been defined properly, given your weird views on cardinality and lack of understanding of the usage of words in proper mathematics youy should at least try to explain what you mean, though you will fail almost surely.
 

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