An accurate representation of Irrational and rational numbers

[Zurtex]

$\pi$ is just a constant, like 1. On a circle if you have a diameter of 10 then you will have a circumference of $10\pi$, if you have a diameter of $1 / \pi$ then you will have a diameter of 1.

The circumference of a circle divided by its diameter will always equal pi, no matter what the size of the circle is. So $\pi$ is just a number.

 

[Hurkyl]

So, is this constant is the "place" of pi on the real line?

Yes; this constant IS pi.

This is exactly what i mean, the pair(circumference,diameter) can be in any "place" on the real line as long as they stick together by their constant ratio.

I can't figure out what you mean in any part of this sentence.

but infinitely many real-lines

There are indeed infinitely many things called the real line, but they are all the same in roughly the same sense that 1, 1, and 1 are all the same.

But I don't see how this relates to anything you're saying.

 

[matt grime]

This is exactly what i mean, the pair(circumference,diameter) can be in any "place" on the real line as long as they stick together by their constant ratio.

the pair (circumference,diameter) is a pair of real numbers, therefore it isn't a real number. But I think we can translate that sentence to mean: given any real number d (positive) there is another real number, C, which is the circumference of a circle with diameter d, for any such pair the ratio C/d is constant. This constant is what we call pi.

In more general view, from this point of view there is no such a thing like a one real-line made up of fixed numbers, but infinitely many real-lines on top of each other where each real-line has its own 1 and we get a fractal, which its depth is infinitely many real-lines.

Nonsense that sounds dangerously like Organic/WWW/Doron Shadmi.

 

[Dialog]

A Fractal is an invariant self-similarity over infinitely many scales, so what is the reason that we cannot use the fractal model instead of the real-line model?

The advantage of the fractal model is that we can use both relative and/or constant definitions, and by this model the real number system is richer then the constant-only real-line model.

 

[matt grime]

thank you for offering conclusive proof of your identity. the usual rebuttals are valid:
1. you've no clue what the mathematical meaning of any of the words you use is
2 you're about to redefine a definition which isn't how things are done
3. you're not actually offering a definition in any mathematical sense just offering subjective opinions

 

[Dialog]

Matt,

Please response to all what I wrote in the previous post (after refreshing screen)

 

[Janitor]

that sounds dangerously like Organic/WWW/Doron Shadmi- Matt

Those little hairs on the back of my neck too were starting to rise.

 

[Hurkyl]

This does not belong here, Organic or not.