An accurate representation of Irrational and rational numbers

[matt grime]

pi can be any 'place' on the real line? of course not, if we must think of it as some physical object, going left to right, positive to negative, then pi is always to the right of all of the following numbers:

3, 3.1, 3.14, 3.141,...

and is in fact the sup of that set, which would be one definition of pi as a real number (dedekind cut)

why do you think pi can be any place on the real line? (ie be any element of the real numbers?)

 

[Dialog]

Because if the diameter can be any number, then pi (as you wrote) is the ratio of a circle's diameter to its circumference.

Therefore pi can be found in any "place" on the real line, which means, we only care for the ratio and not for any particular value.

 

[Hurkyl]

The diameter can be any number. The circumference can be any number. The ratio of the two is a constant; it can only be one number.

 

[matt grime]

Because if the diameter can be any number, then pi (as you wrote) is the ratio of a circle's diameter to its circumference.

Therefore pi can be found in any "place" on the real line, which means, we only care for the ratio and not for any particular value.

usually in a 'therefore' the consequent is implied by the antecedent. I don't see anything that can remotely justify that assertion mathematically. pi is fixed, the ratio between a circle's circumference and diameter is independent of the circle, in the sense that it is the same for any two circles.

 

[Dialog]

The diameter can be any number. The circumference can be any number. The ratio of the two is a constant; it can only be one number.

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

the ratio between a circle's circumference and diameter is independent of the circle, in the sense that it is the same for any two circles.

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.

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.

 

[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.