Is Pi Infinite and What Does It Mean for Science?

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Pi is an irrational number, meaning its decimal representation is infinite and non-repeating, while its value is not infinite as it can be approximated by rational numbers like 22/7. The discussion highlights that despite calculating over 200 billion digits of pi, no repeating pattern has been found, reinforcing its transcendental nature. Participants clarify that while rational numbers have repeating decimals, pi does not, and the concept of "pattern" in this context is complex and not easily defined. There is speculation about whether pi could be normal, which would imply a different kind of pattern, but this has not been proven. Ultimately, pi's infinite digits continue to intrigue mathematicians and computer scientists alike.
  • #51
If any number is a ratio to some fundamental that is itself finite, how can that number be said to be finite? Y'all might be right in your assertions but, with all due respect, I'm not going to take your word for it. Saying that pi is finite is like saying that the sky is finitely blue.
 
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  • #52
Originally posted by Donde (let's stop kidding ourselves, shall we?
Saying that pi is finite is like saying that the sky is finitely blue.

What are you talking about? Earlier in this very thread, you acknowledged that p is less than 4. Of course it is finite, by your own admission!

p is simply the ratio of the circumference of a circle to its own diameter. Consider any given circle. Since the circumference is not infinite and the diameter is not zero, p is finite.

This question was answered in the first two posts. Why on Earth is this silly debate still going on?
 
  • #53
Crackpot rule #1: when you make up your own language, no one can ever prove you wrong!
 
  • #54
If any number is a ratio to some fundamental that is itself finite, how can that number be said to be finite?

By proving that number satisfies the definition of finite.


Y'all might be right in your assertions but, with all due respect, I'm not going to take your word for it.

We're not asking you to take our word for it... there's a reason we use something called a "proof".


Saying that pi is finite is like saying that the sky is finitely blue.

Is it? In what way?
 
  • #55


Originally posted by selfAdjoint
Physics assumes space is a continuum and that the values it discusses can take on all real numbers. The exception is action, which can only take on integer multiples of h.

i know that in Bohr-Sommerfeld quantization, this was the approach, but does that have any resemblance to modern quantum theory? i have not heard said about modern quantum theory that the action must be discrete. i would be surprised to find this is true.
 
  • #56
The word "infinite" has a very specific mathematical meaning. No number that falls between 3 and 4 can ever satisfy that meaning. What else is there to talk about?

I mean really, even from a common sense viewpoint, if you asked any person with an IQ over 90 if "infinite" was bigger than 4, what do you think the right answer would be?
 
  • #57
Is it your contention that a circle with a radius of 1 meter contains within it an infinite amount of area? Can a silo that is 4 Meters in diameter and 10 meters high hold an infinite amount of grain? How much coffee can I fit in my cup? Is the volume of my cup equal to the volume of the silo? How large is a baseball?

If this discussion started pi hours ago and ends pi hours from now, does that mean that we are half-way done? Or will it go on forever...?
 
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  • #58


Originally posted by Tom
What are you talking about? Earlier in this very thread, you acknowledged that p is less than 4. Of course it is finite, by your own admission!

p is simply the ratio of the circumference of a circle to its own diameter. Consider any given circle. Since the circumference is not infinite and the diameter is not zero, p is finite.

This question was answered in the first two posts. Why on Earth is this silly debate still going on?

Tom, 1) Please do not put words in my mouth. I have never admitted to any such (ridiculous) thing as pi being finite.

2) If pi were the "finite" value for describing ratio of circumference to diameter, are you then saying that there is no other value that is capable of describing that same relationship? For if there were, then the pi ratio could not possibly be finite, could it?
 
  • #59
1) Please do not put words in my mouth. I have never admitted to any such (ridiculous) thing as pi being finite.

You have admitted that pi satisfies a condition which is (one) definition of finite.


If pi were the "finite" value for describing ratio of circumference to diameter, are you then saying that there is no other value that is capable of describing that same relationship?

There is no other value that describes the relationship, but that has nothing to do with the finiteness of pi.


By Finite we mean that both ends of some interval are reachable.

No, Organic, that is what you mean, not what we mean.



Anyways, Jug: If you want to talk math, then do so. If you want to continue talking about your own personal ideas and theories, I suggest moving over to an appropriate forum, such as Theory Development or one of the Philosophy forums.
 
  • #60
Jug,

Learn to read, will you please? I said that you admitted to pi being less than 4. That automatically means that it is finite.

Here is where you said it:

Originally posted by Jug
Pi cannot possibly be bigger than 4. Prove that 4 is finite.
 
  • #61
No, Hurkyl, I have not described any finite condition and I don't think you can either. And yes, there ARE other values to describe the same relationship as does pi. Because you (et al) do not believe that does not make it untrue.

As to your dictum, I was referred to this site as being a premier science forum...and I do find it to be that...trusting it may not go the way of so many others by the elitist attitude of a few. I'm here only to learn and hopefully to find some way to contribute.
 
  • #62
If you are here to learn, then why don't you tell us what you think it means for a real number to be finite and/or infinite, then we can all debate the issue, and perhaps we can all learn something. There are several good mathematicians who've posted in this thread all expressing surprise at the notion that pi is infinite, which means not finite. In what way is pi not a finite number, whatever that might mean? Perhaps we cna then explain to you what the more sensible name for this property is.

And why is pi a fundamental (wavelength)? pi is dimensionless and wavelengths aren't, if we're going to think of physics.
 
  • #63
Originally posted by Jug
No, Hurkyl, I have not described any finite condition and I don't think you can either. And yes, there ARE other values to describe the same relationship as does pi. Because you (et al) do not believe that does not make it untrue.

As to your dictum, I was referred to this site as being a premier science forum...and I do find it to be that...trusting it may not go the way of so many others by the elitist attitude of a few. I'm here only to learn and hopefully to find some way to contribute.
That doesn't make any sense. Are you actually claiming that pi and some other value BOTH define the same ratio? If so, what it is?
 
  • #64
Jug,
Is it your position that you are offering rigorous proof that infinity lies between +3 and +4 on a real number line?
 
  • #65
Sorry if I'm covering ground already well and truly stomped, but... Someone mentioned something along the lines of "Pi isn't infinite because it's less than 4". Now, I'm truly crap at maths, but how the heck is being less than four proving that something isn't infinite? There are infinite numbers between 3 and 4. There are infinite numbers between 3.99999999999 and 4. It depends entirely on how much time you want to waste going down to smaller and smaller numbers.
 
  • #66
Originally posted by Adam
Now, I'm truly crap at maths, but how the heck is being less than four proving that something isn't infinite? There are infinite numbers between 3 and 4. There are infinite numbers between 3.99999999999 and 4. It depends entirely on how much time you want to waste going down to smaller and smaller numbers.

Because a real number a is said to be finite if there exists another real number x so that a < x. It is a definition, not something that is out in the open or in need of debating!

Also, "There are infinitely many numbers between 3 and 4". What does that proof? Just because there are an infinite number of numbers does not mean that every (or any) single number is infinite.

Discussions such as these could be avoided if people took the trouble to read an elementary math book before arguing about this stuff...
 
  • #67
adam,
what number lies between 3.999... and 4?
 
  • #68
I went out and bought lunch, paid with a ten dollar bill, and I got $3.14 cents back...I didn't realize I was so close to having infinite money...who knew?
 
  • #69
Originally posted by Dimitri Terryn
Discussions such as these could be avoided if people took the trouble to read an elementary math book before arguing about this stuff...

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).
 
  • #70
No, Hurkyl, I have not described any finite condition and I don't think you can either. And yes, there ARE other values to describe the same relationship as does pi. Because you (et al) do not believe that does not make it untrue.

As to your dictum, I was referred to this site as being a premier science forum...and I do find it to be that...trusting it may not go the way of so many others by the elitist attitude of a few. I'm here only to learn and hopefully to find some way to contribute.


Which is why I suggested https://www.physicsforums.com/forumdisplay.php?s=&forumid=95. Part of what makes Physicsforums work is that we have different subforums for different topics and methods of inquiry.
 
  • #71
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
 
  • #72
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'...
 
  • #73
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?
 
  • #74
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.
 
  • #75
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.
 
  • #76
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.

Code: 
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.
 
  • #77
no, pi is not infinite...it is a spesific value.

is pi irrational?

yes.
 
  • #78
Hi modmans2ndcoming,

no, pi is not infinite...it is a spesific value.
Please give some examples to what you call infinite and not infinite.
 
  • #79
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.

Code: 
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 ...
 ...
 
  • #80
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).
 
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  • #81
And what if I take for example the binary representation of Pi and define
Code: 
 b = {'1','1','1','1','0','0',...}
 N = { 1 , 2 , 3 , 4 , 5 , 6 ,...}
 
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  • #82
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.
 
  • #83
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.
 
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  • #84
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.
 
  • #85
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.
 
  • #86
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:

Code: 
 b = {'1_1','1_2','1_3','1_4','0_1','0_2',...}
 N = {  1 ,   2 ,   3 ,   4 ,   5 ,   6 ,...}
 
  • #87
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
 
  • #88
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.
 

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