Exploring the Infinity of Pi: A Scientific Perspective

[matt grime]

Originally posted by Organic
Let us notated this case by (0,1) which mean that no quantity of sub-intervals that existing between 0 and 1, can reach 0 and/or 1.

We can represent the fractional side of our number system fraction representation of pi...

idiot

 

[matt grime]

Originally posted by ahrkron
I agree.

I think they also need to understand the role of definitions. Many people try to "challenge" definitions because they think there "should be more to it". That in itself shows that they don't understand what the concept of "definition" means in math (and science).

please can every moronic crank have this perfect synopsis tatooed on their forehead. preferably in mirror writing so they see it every day when brushing their teeth. In particular Organic the uber crank of PF, who has accused me of 'just playing with definitions'...

 

[Adam]

Originally posted by Michael D. Sewell
adam,
what number lies between 3.999... and 4?

Doesn't it depend on how far down in scale you wish to go? As I said, I'm crap at maths, but it seems to me that 3.9901 is smaller than 3.9902. 3.9900000001 is smaller again. Since I can go down in scale as much as I want, there's no end to it. Is this not right?

 

[Kalimaa23]

Again, learn some basic facts first.

The notation 3,99... means an unending series op 9's behind the comma. And this is, in the limit, equal to 4, so there is nothing between 3,99... and 4.

 

[Adam]

Sorry, but in my country, the ellipses do not mean that. To represent an unending series after the decimal point, we place a dot above the last (right-most) digit.

 

[Organic]

When we determine what is 1 we can change our scale by comparing it to 1.

The results are ordered by a place value fractal structure constructed by base_value^power_value.

For example let us use the fractal structure that constructed by 2^-power_value, where the power_value is any negative integer.

The left side of pi floating point = 3 times 1

But the interesting side is the fractal tree that exists in the right side of the floating point of pi.

When using this fractal representation method, we can clearly see that pi right value is a unique and infinitely long path that goes through infinitely many levels of this fractal, and this path cannot reach 0.

Z- ={-1-2-3-4,...}
     2 2 2 2
     ^ ^ ^ ^
     | | | |
     v v v v
          /1 ...
         1 
        / \0 ...
       [b]1[/b]   
       /\ /1 ... 
      /  [b]0[/b]
     /    \[b]0[/b] ... 
     [b]1[/b]    
     \    /1 ... 
      \  1 
       \/ \0 ... 
       0  
        \ /1 ...
         0
          \0 ...
[b]3.[/b]---------------------> [b]0[/b]
          /1 ... 
         1
        / \0 ...
       1  
       /\ /1 ...
      /  0 
     /    \0 ...
     0    
     \    /1 ...
      \  1
       \/ \0 ...
       0  
        \ /1 ...
         0
          \0 ...
 ...

The path 1100... is the beginning of 01 fraction representation of pi.

But the important thing here is the fractal structure that can be used as common system that can help us to define the deep relations between pi and another interesting numbers.

 

[modmans2ndcoming]

no, pi is not infinite...it is a spesific value.

is pi irrational?

yes.

 

[Organic]

Hi modmans2ndcoming,

no, pi is not infinite...it is a spesific value.

Please give some examples to what you call infinite and not infinite.

 

[Organic]

Pi is a specific value or what I call a specific path in a never-ending fractal.

By never-ending fractal I mean that no node in this tree is a "pure" child.

Shortly speaking, each node is a father.

Z- ={-1-2-3-4,...}
     2 2 2 2
     ^ ^ ^ ^
     | | | |
     v v v v
          /1 ...
         1 
        / \0 ...
       [b]1[/b]   
       /\ /1 ... 
      /  [b]0[/b]
     /    \[b]0[/b] ... 
     [b]1[/b]    
     \    /1 ... 
      \  1 
       \/ \0 ... 
       0  
        \ /1 ...
         0
          \0 ...
[b]3.[/b]---------------------> [b]0[/b]
          /1 ... 
         1
        / \0 ...
       1  
       /\ /1 ...
      /  0 
     /    \0 ...
     0    
     \    /1 ...
      \  1
       \/ \0 ...
       0  
        \ /1 ...
         0
          \0 ...
 ...

 

[modmans2ndcoming]

infinite:

a system that has no Maximum number of descrete elements.

pi itself is not a system, it is an element of the real number set.

the fractal graph of pi IS infinite because you are talking about a SYSTEM or SET.

in the case of numbers, the set of all natural numbers is infinite for X>= 1

in the case of a fractal graph of pi, the set of all nodes in infinite as well.

but pi itself is a value WRT the set of all real numbers with a value that exists on the interval (3.141, 3.142).

 

[Organic]

And what if I take for example the binary representation of Pi and define

 b = {'1','1','1','1','0','0',...}
 N = { 1 , 2 , 3 , 4 , 5 , 6 ,...}

 

[modmans2ndcoming]

do you understand what I am saying?

I am saying that the term infinite is dependent on the Set you are talking about.

you can create a set that is derived from pi, and that set is infinite, but the number pi that exists in the set of real numbers is not infinite.

 

[Organic]

Do you mean that R is the "global" infinity and pi is some unique element in R?

But if we construct a collection of infinitely many finite substrings taken from pi, then pi is the "global" infinity.

 

[modmans2ndcoming]

First off, pi is pi, 3.14159 is just a nice approximation of it.

also, let's say that you created a set of all possible approximations of pi...yes, that set will be infinite, but that does not make the discrete value of pi infinite.

you are having trouble it seems distinguishing between a set derived from a discrete value, and the discrete value itself.

the term infinity can only apply to a set of elements, not a specific element, which the number pi is.

so, again, let me try and say this as clearly as possible, the number pi is just an ELEMENT of the set of Real Numbers. it can not, by the definition of infinity, be infinite.

you have correctly identified though, that it is possible to derive a set from pi which is infinite, but that set is not equal to pi because a set can never be equal to a number, a set can only be equal to another set.

 

[matt grime]

Originally posted by Organic
Do you mean that R is the "global" infinity and pi is some unique element in R?

But if we construct a collection of infinitely many finite substrings taken from pi, then pi is the "global" infinity.

as we can do this for every number in R, everyone of them is your 'global infinity' whatever particularly silly idea that might be.

 

[Organic]

you have correctly identified though, that it is possible to derive a set from pi which is infinite, but that set is not equal to pi because a set can never be equal to a number, a set can only be equal to another set.

There is no limit to a content of a set if it can be compared with N members, therefore this set is a legal set:

 b = {'1_1','1_2','1_3','1_4','0_1','0_2',...}
 N = {  1 ,   2 ,   3 ,   4 ,   5 ,   6 ,...}

 

[chroot]

Moderators, how much longer does this thread need to be left in the General Math section? The answer to the original question was given many pages ago.

- Warren

 

[Hurkyl]

It took a turn for the better this morning. However, now that it's turned for the worse again, I agree, this is a good time to lock it.