- #106
Lama
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Let us add some more details.
Let us say that every unique name along the real line is represented by a single symbol.
In this case there is 'no room' for Cantor's diagonal method and we cannot conclude that there is a difference between the single symbols of the entire real line and the single symbols of the natural numbers.
But this is not correct because, when we ignore the fractal nature of the real line and care only about its magnitude, then in this case any unique symbol can be mapped only to itself.
In this case, the unique symbols that represent only the natural numbers cannot have the magnitude of the entire real line.
The mistake of standard Math point of view is: when it finds a 1-1 and onto between some set of infinitely many elements to some proper subset of it, it is not aware to the fact that it uses the fractal property of the number line.
If we aware to the simple fact that the magnitude of the number line is not depended on its fractal nature, then and only then we can clearly understand (by researching a one and only one arbitrary level of this fractal) that there cannot be any 1-1 and onto between some set of infinitely many unique symbols, to a proper subset of it.
Strictly speaking, the absolute/relative picture of the real-line is simpler and richer than the standard point of view.
Another important side effect here is that our simple intuitions are not forced to deal with weird states.
Let us say that every unique name along the real line is represented by a single symbol.
In this case there is 'no room' for Cantor's diagonal method and we cannot conclude that there is a difference between the single symbols of the entire real line and the single symbols of the natural numbers.
But this is not correct because, when we ignore the fractal nature of the real line and care only about its magnitude, then in this case any unique symbol can be mapped only to itself.
In this case, the unique symbols that represent only the natural numbers cannot have the magnitude of the entire real line.
The mistake of standard Math point of view is: when it finds a 1-1 and onto between some set of infinitely many elements to some proper subset of it, it is not aware to the fact that it uses the fractal property of the number line.
If we aware to the simple fact that the magnitude of the number line is not depended on its fractal nature, then and only then we can clearly understand (by researching a one and only one arbitrary level of this fractal) that there cannot be any 1-1 and onto between some set of infinitely many unique symbols, to a proper subset of it.
Strictly speaking, the absolute/relative picture of the real-line is simpler and richer than the standard point of view.
Another important side effect here is that our simple intuitions are not forced to deal with weird states.
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