Is pi infinite?

[pallidin]

Is pi Infinite?

[chroot]

No, \pi < \infty.

- Warren

[Integral]

Further

3.14 < \pi < 3.15

[luther_paul]

What do u mean pi is infinite? the value itself or the digit? if u are talking about the digits, its infinite because it is an irrational number, meaning unending digits. the value itself is not infinite because it has an exact value (22/7).
3.14 < \pi < 3.15
its common sense to say that!peace!

[chroot]

Originally posted by luther_paul
the value itself is not infinite because it has an exact value (22/7).
22/7 is a rational number, and thus has a repeating or terminating decimal expansion. 22/7 is not pi. 22/7 is just a crude approximation sometimes used in place of pi.

- Warren

[pnaj]

luther_paul

Sorry to be picky, but ...it is an irrational number, meaning unending digits ... is not actually true (just in case pallidin gets the wrong idea).

A rational number is any number that can be written m/n where m,n are integers.
So,
1/7 = 0.142857142857142857142857..(142857 recurring)
is rational, but has 'unending ' digits.

In fact, technically,
1/1 = 1.000000000000000000000000..(0 recurring)
has infinitely many digits.

But, for an irrational, there will never be a recurring pattern in the expansion, as for the rationals.

Another way to look at it is this.

Suppose you trying to calculate the decimal expansion of 1/7 by hand (or by any other method). Once you'd got to the first recurrence of the sequence (142857) you would stop, because it's for certain that the pattern will recur infinitely.

So far, over 200 billion digits of PI have been calculated ... no pattern yet.

[pnaj]

There's a BBC programme that discusses infinity ...

In Our Time - Infinity (http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20031023.shtml)

[master_coda]

Originally posted by pnaj
So far, over 200 billion digits of PI have been calculated ... no pattern yet.

And there never will be a pattern. Just in case anybody wasn't clear about that from the above posts.

[luther_paul]

pnaj
thanks for the info... i got that wrong, it must've been nonterminating and non-recurring/nonrepeating...

warren
ur right 22/7 is just a crude estimation of pi, but i used 22/7 to show that pi has an exact value, not infinity.. the topic is about pi being an infinite.

thanks, by the way..

[mouseonmoon]

Originally posted by master_coda
And there never will be a pattern. Just in case anybody wasn't clear about that from the above posts.

well, there
seems to be a pattern of PI repeating here..(smile)

anyway-what's the 'fartherest out' that's been found for a 'repeater'
(hope this isn't an 'irrational' question--i'm simply guessing someone's played around
with the idea ie. recurring patterns)

or,in different words, what 'number' begins its pattern sequence with the greatest expansion?
or/and, --what rational number has been found with the 'longest pattern'?

what am i asking?....how long can a sequence be?....is there any formula that 'predicts' these patterns etc.....anything along these lines-who's written about this? (or 'wierd' math in general--who was the guy who 'proved' 1+1 didn't equal 2 ?--did anyone ever prove he was wrong??)

why am i asking?....well, why has PI been taken to over 200 billion digits?
Can one really say, 'it will never repeat'?
seriously...

[pnaj]

No, you can't say there will never be a pattern, just that you cannot predict that there will be one, even after calculating the first 200 billion digits.

One could positively show that it is terminating ... if you found the pattern.

One cannot positively show that there is no pattern.


Apart from the massively small chance that a pattern does emerge, the main reason for looking seems to be bench-testing of more-and-more powerful computers.

P.

[krab]

Originally posted by pnaj
No, you can't say there will never be a pattern, just that you cannot predict that there will be one, even after calculating the first 200 billion digits.

One could positively show that it is terminating ... if you found the pattern.

One cannot positively show that there is no pattern. That ain't right. Pi was proved to be a transcendental number already way back in 1882. Therefore, no pattern. More info. (http://en.wikipedia.org/wiki/Pi)

[HallsofIvy]

Originally posted by mouseonmoon
what rational number has been found with the 'longest pattern'?

what am i asking?....how long can a sequence be?....is there any formula that 'predicts' these patterns etc.....
Assuming that by "pattern" you mean section of digits that then repeats, the rational number m/p where p is prime and m< p will have repeating section with p digits. Since there exists arbitrarily large prime numbers, the repeating section can be as large as you please.

Originally posted by pnaj
No, you can't say there will never be a pattern, just that you cannot predict that there will be one, even after calculating the first 200 billion digits.
What exactly do you mean by "pattern"? Most of the responses here are using it to mean a section that repeats.
It is fairly easy to show that if the decimal expansion of a number eventually consists of a section that then repeats, that number is rational. It is also fairly easy to show that pi is not rational and so never repeats.

[master_coda]

When I said that pi doesn't have a "pattern" I meant that it does not repeat. Almost any other notion of pattern is difficult to define mathematically.

[chroot]

Originally posted by HallsofIvy
Assuming that by "pattern" you mean section of digits that then repeats, the rational number m/p where p is prime and m< p will have repeating section with p digits.
Is this true? How about 1/3, which has only one repeating digit? Or 1/7, which has six?

- Warren

[lethe]

Originally posted by master_coda
When I said that pi doesn't have a "pattern" I meant that it does not repeat. Almost any other notion of pattern is difficult to define mathematically.

there are lots of irrational numbers that do have patterns. my favorite example is this one:

0.1101001000100001000001.....

one way to define whether a number has a pattern is to show that the number is normal. a number is normal if, loosely speaking, any finite sequence of digits appears about as frequently as it would for a random sequence of digits

it is probable that pi is normal, but not proved, so in fact, there may be a pattern. in fact, people sometimes look for patterns in the digits of pi. we simply don t know if it has any. remember the movie Pi? i think that guy found the torah in the digits of pi, or something (of course, it was a work of fiction).

[pnaj]

HallsofIvy,
Did you see the original question?

We were all trying to help someone understand the nature of the difference between a rational number and a irrational one.

So, I wouldn't dispute what you say, of course ... you're right ... but I'm not sure how much help ....
Originally posted by HallsofIvy
It is also fairly easy to show that pi is not rational and so never repeats.
... would really be to someone who might not really know what 'rational' is.


================
Also, krab and master_coda, thanks for pointing out that PI has been proved to be transcendental (and thus not rational), I could have misled someone there ... I wasn't precise enough. What I should have said was ...

Suppose you didn't know whether PI was rational or not.

Then ...
Originally posted by pnaj
No, you can't say there will never be a pattern, just that you cannot predict that there will be one, even after calculating the first 200 billion digits.

One could positively show that it is terminating ... if you found the pattern.

One cannot positively show that there is no pattern.
... makes more sense.

What I trying to get our friend to get the gist of was this:

If you look at the decimal expansion of any particular number upto to squillionth digit, and not see a terminating-repeating sequence of digits, that does not mean that is not rational. You gain no information that will help you predict whether it is rational or not.


Cheers,
P.

[master_coda]

Originally posted by lethe
there are lots of irrational numbers that do have patterns. my favorite example is this one:

0.1101001000100001000001.....

one way to define whether a number has a pattern is to show that the number is normal. a number is normal if, loosely speaking, any finite sequence of digits appears about as frequently as it would for a random sequence of digits

it is probable that pi is normal, but not proved, so in fact, there may be a pattern. in fact, people sometimes look for patterns in the digits of pi. we simply don t know if it has any. remember the movie Pi? i think that guy found the torah in the digits of pi, or something (of course, it was a work of fiction).

But I could argue that a number has a pattern as long as we have an algorithm for generating its digits.

Perhaps it's best to avoid the use of the word "pattern", since it seems hard to define properly.

[chroot]

Originally posted by master_coda
But I could argue that a number has a pattern as long as we have an algorithm for generating its digits.
There are lots of algorithms to generate the digits of pi......

- Warren

[pnaj]

Sorry, probably my fault for introducing the dreaded 'pattern' word.

[mouseonmoon]

first, let me thank krab for the Wikipedia link-
love it and been ' lost in delight ' ever since!!

(and speaking of logarithms-John Napier invented 'em-what a character! and math was 'just a hobby' for him-
http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Napier.html

and speakin' of patterns:
The infinite continued fraction expansion of e contains an interesting pattern that can be written as follows:
e= {1;1,1,2,1,1,4,1,1,6,1,1,8,1,1 ...}
(which was described by Richard Feynman as "The most remarkable formula in mathematics"!)

But back to the original post in this thread-is Pi infinite?-

the mind boggles-my does anyway.....

seems there 'could be' an 'infinite' number of 'patterns' in the 'expansion' of Pi (are there absolutely no patterns within the 200 billion digits so far generated?-seems impossible)--yet it 'cannot' 'in fact' 'repeat' (("repeat": as it is proven to be transcendent))...holding in thought the computer
laboring on with the 'expansion' of Pi to 'infinity'....

Has anyone put this question to one of those gifted individuals known as 'idiot savants'? I've heard where some are able to 'instantly' perform calculations of immense complexity--i am not aware of anyone with this ability today.......(perhaps it would be inhumane to attempt such a thing-let me express my vote against such an 'experiment'!)

i've reached my limit...sparkplugs burnt out, confused astoundment, brain cells fused........
excuse me, i need to find the 'Dear Santa' forums....oh Dorothy!!

[krab]

Originally posted by pnaj
Sorry, probably my fault for introducing the dreaded 'pattern' word. Don't be sorry. As Warren points out, with a sufficiently broad definition of pattern, pi does have a pattern. Just no repeating digits.

[lethe]

Originally posted by krab
Don't be sorry. As Warren points out, with a sufficiently broad definition of pattern, pi does have a pattern. Just no repeating digits.

yes, if you make the definition of "pattern" so broad as to be trivial and useless, so that all things are patterns, then pi has a pattern. on the other hand, there exist patterns which are not trivial and are mathematically well defined. one example is repeating sequence of digits, which pi does not contain. there are other patterns which pi may have. it is not known whether it does or does not.

[selfAdjoint]

ANd of course pi escapes patterns more general than repeating digits, since it's transcendental, i.e. not the solution of any polynomial equation with rational coefficients.

So both square root of two and pi lack repeating digits, but square root of two will be found to have a more subtle pattern deriving from its definition as a solution of x2 = 2, but you will never be able to find such a pattern in pi.

[moshek]

pnaj,

With the eye's of non Euclidian mathematics
that see alway's mathematics as
"One whole organism" ( Hilbert vision 1900)
your original question does pai infinity?"
became significant when we present pi in base 16
and this close a circle of 5,000 years voyager to find pai.


Moshek
[:))]

[lethe]

Originally posted by selfAdjoint
ANd of course pi escapes patterns more general than repeating digits, since it's transcendental, i.e. not the solution of any polynomial equation with rational coefficients.

So both square root of two and pi lack repeating digits, but square root of two will be found to have a more subtle pattern deriving from its definition as a solution of x2 = 2, but you will never be able to find such a pattern in pi.

for example, root 2 repeats digits in its continued fraction representation, whereas pi does not.

[krab]

Originally posted by lethe
yes, if you make the definition of "pattern" so broad as to be trivial and useless, so that all things are patterns, then pi has a pattern. That's not what I mean. A possible non-trivial broad definition of pattern is simply a finite algorithm for finding the digits. The number you gave as your favourite transcendental number can be written

\sum_{n=0}^\infty (.1)^{1+n(n+1)/2}

and only has a readily discernable pattern because of the "coincidence" that (1/10) appears raised to a power, and we represent our numbers on the base 10. Pi can be defined for example by the following "pattern":

\pi=8\,\sum_{n=0}^\infty [(4n+1)(4n+3)]^{-1}

=8\left[{1\over 1\times 3}+{1\over 5\times 7}+{1\over 9\times 11}+...\right]

This, admittedly, won't have a pattern among the digits no matter what the base is; but it's still a pattern in the broad (but non-trivial) sense.

[toasty]

Originally posted by krab
That ain't right. Pi was proved to be a transcendental number already way back in 1882. Therefore, no pattern. More info. (http://en.wikipedia.org/wiki/Pi)

Sorry to be reviving this but can you explain exactly what you mean by 'trancendental''?

Can you also give the source, and if possible a short summary of the proof in simple language?

Thank You

[matt grime]

transcendental numbers are those that are not the root of any polynomial with integer coefficients (equivalently with rational coeffecients)

e and pi are transcendental. numbers that are not transcendental are called algebraic.

i'm not sure the proofs i've seen are considered nice, especially if this is the first time you've seen the definition of algebraic and transcendental.

almost all numbers are transcendental - there are only a countable number of algebraic numbers so there must be an uncountable number of transcendentals.


Hilbert's proof of the transendence of e runs to about two pages of Le Veque's Fundamentals of number theory and doesn't really involve anything useful. He says 'it is as elegant as it is mysterious' and involves integrating by parts.

a similar proof for pi was also given by hilbert.

there is a 1976 springer-verlag lecture series in mathematics by Mahler which gives several proofs of these facts, though I've never seen it.


If you wish me to I can reproduce the e proof and give you another proof for pi that can be found in a lot of galois theory textbooks under the stuff about transcendental extensions.

[toasty]

Sorry to bring you back to this one !

I found the page with the links which I neglected to click on before because I did not notice it!

However it does neatly tie in with some other things.

Transcendental as I recall was used about things 'inducted' by limited information. A good example is the proof that 0 may not be a demoninator.

[Tom Mattson]

I'm just glad Donde isn't here.

[Integral]

Originally posted by Tom
I'm just glad Donde isn't here.

Funny you should menttion that.. I was thinking of him also..

[Jug]

Originally posted by Tom
I'm just glad Donde isn't here.

What is the intrinsic value of any number, transcendental, irrational, etc., beyond what it can prove by empirical evaluation? For example, can the degree of arc be better defined by the purely abstract irrational pi than it can by the rational value of 355/113?

[selfAdjoint]

Originally posted by Jug
What is the intrinsic value of any number, transcendental, irrational, etc., beyond what it can prove by empirical evaluation? For example, can the degree of arc be better defined by the purely abstract irrational pi than it can by the rational value of 355/113?

Yes it can. And when pi comes up in formulas that physicists use, you don't wnat to complicate the logic by assuming pi is some approximation like 22/7 or 355/113, or 3.1416. 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.

What is true is that physicists can never tell whether some particular value they work with is irrational, unless math tells them it is. So pi and e are known to be irrational (and transcendental), but h and alpha are not sure.

[Jug]

Have to disagree, SelfAdjoint. What I hear you saying is that we shouldn't complicate logic with the truth.

But as regards the subject proper, pi is of course infinite. In that regard then, and not being a maths person myself, I can only relate to the basics from which our mathematics derive - the perfect ratios given by Pythagoras: 0:1:1:2:3:4 - and where it is assumed that the cipher was intended by Pythagoras to represent the finite condition; which is to suggest that the cipher in place of denoting a lack of magnitude might in fact denote total magnitude.

My contention then is that the true ratio of pi cannot be arbitrarily determined but must in fact conform exactingly to some full set of ratios describing the finite condition. Just some thoughts on the thing....

[matt grime]

If that is what you believe, Jug, then you are commiting several common mistakes. The first is presuming that there is something special about decimal expansions (or any other base). pi is as easily descibed, and as easily calculted as 1/3. That is to say, given a line with integer units marked on it pi and 1/3 are just as easily located. in fact, I'd say pi is more easilyl located; look at the proof of existence of the first transcendental number.

pi, 1/3 sqrt(2) are just symbols reprsenting some cuachy sequence of rational numbers, they are all as useful as each other, pi perhaps more so. How is 22/7 more accurate than pi?

pi is not infinite. Its decimal expansion is not eventually periodic, but that isn't important. I can more easily construct sqrt(2) than 1/3 given a ruler and compass.

The rest of your post is mostly uninterpretably to my mind.

[Hurkyl]

My contention then is that the true ratio of pi cannot be arbitrarily determined but must in fact conform exactingly to some full set of ratios describing the finite condition. Just some thoughts on the thing....


If you mean that &pi; is the limit of a sequence of fractions that approximate it, it may interest you to know that one model of the real numbers is just that; a real number is a sequence of 'converging' fractions.

[Jug]

MG, we appear to be equally incoherent to one another. By example, you ask:

1) "How is 22/7 more accurate than pi?" It is not, regardless of what value you give to pi.

2) "Pi is not infinite." Then what is its finite value?

[Hurkyl]

"Pi is not infinite." Then what is its finite value?

Pi.


pi is of course infinite.

Then prove it's bigger than 4.

[Jug]

Originally posted by Hurkyl
Pi.




Then prove it's bigger than 4.

Pi cannot possibly be bigger than 4. Prove that 4 is finite.

[matt grime]

Originally posted by Jug
MG, we appear to be equally incoherent to one another. By example, you ask:

1) "How is 22/7 more accurate than pi?" It is not, regardless of what value you give to pi.

2) "Pi is not infinite." Then what is its finite value?

I don't think 'equally' is the word you want.

First as pi is a number between 3 and 4, it is not infinte, is it? It is finite. If you think it is infinite, then you do not know what infinite means.

You were the person that suggested that some fraction was 'better' than pi.

I can tell you what pi is exactly: it is the ratio between a circle's diameter and its circumference. Just as sqrt(2) is the number (positive) which squares to two, just as 22/7 is the number which when multiplied by 7 gives the answer 22.

Look at Tim Gowers's discussions on what is solved when one solves an something.

Your replies to Hurkyl's post indicate that you ought to learn about things that you are speaking on.

[Hurkyl]

The definition of finite for ordinal numbers is:
n is finite if and only if n is a natural number.
4 is a natural number, thus as an ordinal number, it is finite.


The definition of finite for the extended real numbers is:
n is finite if and only if n is a real number.
4 is a real number, thus as an extended real number, it is finite.


The definition of finite for hyperreal numbers is:
n is finite if and only if there is a natural number m with -m < n < m.
5 is a natural number, and -5 < 4 < 5.
Thus, as a hyperreal number, 4 is finite.


The definition of finite for sets is:
S is finite if and only if it is bijective to a natural number1.
4 is a natural number, and is bijective to itself.
Thus, as a set, 4 is finite.


Um... I can't think of any other (standard) mathematical terms labelled 'finite' or 'infinite' that apply to something labelled '4'. Is that good enough for you?


Hurkyl

1: In set theory, there is a "standard" model for the natural numbers in terms of sets. Since it is fairly common to label these sets by the symbol used to label the natural number it models, I figured I might as well include this definition too.

[Jug]

What y'all say sounds reasonable, standard and as curricula for an abstract, logarithmic progression of numbers for the defining of pi; yet, IMO, showing no relationship to any finite conclusion, particulrly as pertaining to a numbers set of such finality. How can you say that the pi ratio is finite when it merely represents one particular ratio of such finality?

I have to hold to the Pythagorean concept of mathematics as the science of describing exacting relationships. The concept, at least by my interpretation, allows for but one finite condition, all participles of which emanate from a finite fundamental and in return to which can only find final resolve. Furthermore, I would suggest that all participles emanating from the fundamental must demonstrate a repetitive numbers set of infinite progression. In short, whatever its value the pi ratio can only be infinite.

[HallsofIvy]

"Furthermore, I would suggest that all participles emanating from the fundamental must demonstrate a repetitive numbers set of infinite progression."

Isn't it remarkable how one can put together a sentence that sounds like it actually means something!

There are several problems I have with that sentence. First is the fact that "fundamental" is an adjective, not a noun so I cannot find a subject in it. On the other hand "numbers" is a noun rather than an adjective so I have no idea what "a repetitive numbers set" is. I guess it would be too much to point out that a "set", by definition, cannot be "repetitive".

Finally, I can't see how a "conclusion" can be either "finite" or infinite. What I would like is for Jug to tell us explicitely what definitions of "finite" and "infinite" he is using. They are clearly not the standard ones.

[Hurkyl]

I know the first digit in the decimal representation of pi is 3. Therefore, I know -4 < pi < 4. Thus, pi is finite.


If you would like to supply an alternative definition of "infinite" (either by saying what "infinite" is, or properties "infinite" has), we can discuss whether pi is finite or infinite with respect to that definition.

However, even if pi is infinite according to your definition, that does not change the fact that pi is finite according to the definitions I quoted.


(And for the record, your post made very little sense)

[Jug]

Originally posted by HallsofIvy
"Furthermore, I would suggest that all participles emanating from the fundamental must demonstrate a repetitive numbers set of infinite progression."

Isn't it remarkable how one can put together a sentence that sounds like it actually means something!

There are several problems I have with that sentence. First is the fact that "fundamental" is an adjective, not a noun so I cannot find a subject in it. On the other hand "numbers" is a noun rather than an adjective so I have no idea what "a repetitive numbers set" is. I guess it would be too much to point out that a "set", by definition, cannot be "repetitive".

Finally, I can't see how a "conclusion" can be either "finite" or infinite. What I would like is for Jug to tell us explicitely what definitions of "finite" and "infinite" he is using. They are clearly not the standard ones.

I was hoping we might avoid the pedantry. By "fundamental" is of course meant fundamental wavelength. Do we really need to engage in a discussion over ordinary physics terms?

As to your claim that a "set" cannot be repetitive, what is 1.185185185....ad infinitum, if not a repetitive set?

[Hurkyl]

I was hoping we might avoid the pedantry. By "fundamental" is of course meant fundamental wavelength. Do we really need to engage in a discussion over ordinary physics terms?

Oh, of course, it was so obvious.


As to your claim that a "set" cannot be repetitive, what is 1.185185185....ad infinitum, if not a repetitive set?

A decimal expansion? A sequence of digits, perhaps?

[matt grime]

the solution of 1000(x-1)-185=x-1?

I'm still also at a loss to understand how a ratio is infinite, in whatever sense you use.


As yoy adopt the pythagorean attitude of exactitude, whatever that might be, can you get more precise than the statement pi is the ratio of the circumference to the diameter of a circle?

[Jug]

Originally posted by matt grime
the solution of 1000(x-1)-185=x-1?

I'm still also at a loss to understand how a ratio is infinite, in whatever sense you use.


As yoy adopt the pythagorean attitude of exactitude, whatever that might be, can you get more precise than the statement pi is the ratio of the circumference to the diameter of a circle?

If any number is the ratio to some fundamental that is itself finite, how can that number be said to also be finite? Y'all may be perfectly right in your assertion but, with all due respect, I'm not going to take your word for it. The academia is ever being corrected.

[matt grime]

With least due respect, are you trying to be a crank or a troll?

You perhaps want to change some of the prepositions in that last post. You at least want to rewrite it so it makes sense, anyway.

1 is finite, I think, though it's rather unclear what you think finite means. It is also a ratio, of 1/1, and I think it's fundamental, in some sense...

[Jug]

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.

[Tom Mattson]

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?

[Zero]

Crackpot rule #1: when you make up your own language, no one can ever prove you wrong!

[Hurkyl]

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?

[lethe]

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.

[Zero]

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?

[Michael D. Sewell]

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...?

[Jug]

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?

[Hurkyl]

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.

[Tom Mattson]

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.

[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.

[matt grime]

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.

[Zero]

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?

[Michael D. Sewell]

Jug,
Is it your position that you are offering rigorous proof that infinity lies between +3 and +4 on a real number line?

[Adam]

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.

[Dimitri Terryn]

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...

[Michael D. Sewell]

adam,
what number lies between 3.999... and 4?

[Zero]

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?

[ahrkron]

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).

[Hurkyl]

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 this forum (http://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.

[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?

[Dimitri Terryn]

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 ...
1
/\ /1 ...
/ 0
/ \0 ...
1
\ /1 ...
\ 1
\/ \0 ...
0
\ /1 ...
0
\0 ...
3.---------------------> 0
/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 ...
1
/\ /1 ...
/ 0
/ \0 ...
1
\ /1 ...
\ 1
\/ \0 ...
0
\ /1 ...
0
\0 ...
3.---------------------> 0
/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, lets 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.