R set magnitude

In summary: By what knowledge do you come to that conclusion?Pease share it with us.In summary, "fixed scale" on the real line refers to a specific scale used to measure the real numbers on the line. The question of how a part of the real line can have the same magnitude as the whole line is answered by showing a 1-1 correspondence or bijection between the two sets. However, the existence of a bijection does not necessarily mean there is a self-similarity between the two sets.
  • #36
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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  • #37
if we take just positive real numbers, the same is true of the right half of the parabola y=x*x, as it is of the tan curve in its principal region. neither is a fractal. or have you just redefind fractal to suit your purposes?
 
  • #38
You do not understand my argument.

I am not talking about the proprty of some function but on the way of how the magnitude of its elements can be the same in any sub-collection of it.

The fractal nature of the magnitude of R collection do not care about the "character" of any function that has the magnitude of R collection.

For example, take any segment of your non-fractal parabola, and the magnitude remains the same.

By using the word "fractal" I mean self-similarity of the magnitude that can be found in any sub-collection of your function.
 
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  • #39
so fractals have nothing to do with it at all? why am i not even moderately surprised?
 
  • #40
Matt, self-similarity of some property (and in this case the magnitude of R collection) which can be found in any arbitrary sub-part of the examined system (and in this case the system is the real-line) is nothing but a fractal, got it?
 
  • #41
so something is a fractal in your new sense if there is a bijection to some proper subset of it? that would be dedekind infinite then, wouldn't it?
 
  • #42
bijection to some proper subset of it is the clearest sign that we have here a fractal.

I think Cantor also used this property.
 
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  • #43
no, it is just dedekind infinite. it doesn't seem reasonable to say it is therefore a fractal, unless you want to redefine the word fractal to mean dedekind infinite, which is what you're are saying
 
  • #44
Dedekind used this property, but he did not know that it is actually the property of a fractal.

Cantor defined the Cantor set, but he did not know that it is a fractal.

Chaos theory was developed after their time.


(Also please pay attantion that our standard place value representation method is also a fractal and also surreal numbers)
 
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  • #45
"it is actually the property of a fractal" oh, that makes it all so much clearer...
 
  • #46
When a collection of elements refers to itself, you can get a fractal.
 
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  • #47
Shemesh, where is that all going? So what if the real line can be represented in different scales.It doesn't mean that you will find "new" properties. If a property of fractals appears with some representations doesn't mean that the real line will have all of the properties of fractals.
 
  • #48
This isn't going anywhere. This is just an attempt to change to meaning of the word fractal to something general and vague for no reason.

If someone was interested in trying to describe a new or interesting idea, they would use the existing terms with their existing definitions instead wasting all their time redefining things so that nobody can understand what they're talking about.
 
<h2>What is "R set magnitude"?</h2><p>"R set magnitude" refers to the magnitude of a set of numbers in the statistical programming language R. Magnitude is a measure of the size or extent of a set, and in R, it is typically calculated using the sum of the absolute values of the numbers in the set.</p><h2>How is the magnitude of a set calculated in R?</h2><p>The magnitude of a set in R is calculated using the sum of the absolute values of the numbers in the set. This means that each number in the set is converted to its absolute value (i.e. its distance from 0 on the number line) and then all of these values are added together to get the magnitude.</p><h2>What is the significance of calculating the magnitude of a set in R?</h2><p>Calculating the magnitude of a set in R can provide useful information about the size and distribution of the data. It can also be used to compare the magnitude of different sets and identify any outliers or extreme values.</p><h2>Can the magnitude of a set in R be negative?</h2><p>No, the magnitude of a set in R is always a positive value. This is because the absolute value function used in the calculation of magnitude always results in a positive value, regardless of the sign of the original number.</p><h2>Are there any other ways to measure the size of a set in R?</h2><p>Yes, there are other measures of size or extent that can be used in R, such as the range, mean, and standard deviation. However, the magnitude of a set is a commonly used measure, particularly when dealing with sets of numerical data.</p>

What is "R set magnitude"?

"R set magnitude" refers to the magnitude of a set of numbers in the statistical programming language R. Magnitude is a measure of the size or extent of a set, and in R, it is typically calculated using the sum of the absolute values of the numbers in the set.

How is the magnitude of a set calculated in R?

The magnitude of a set in R is calculated using the sum of the absolute values of the numbers in the set. This means that each number in the set is converted to its absolute value (i.e. its distance from 0 on the number line) and then all of these values are added together to get the magnitude.

What is the significance of calculating the magnitude of a set in R?

Calculating the magnitude of a set in R can provide useful information about the size and distribution of the data. It can also be used to compare the magnitude of different sets and identify any outliers or extreme values.

Can the magnitude of a set in R be negative?

No, the magnitude of a set in R is always a positive value. This is because the absolute value function used in the calculation of magnitude always results in a positive value, regardless of the sign of the original number.

Are there any other ways to measure the size of a set in R?

Yes, there are other measures of size or extent that can be used in R, such as the range, mean, and standard deviation. However, the magnitude of a set is a commonly used measure, particularly when dealing with sets of numerical data.

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