Talk:Pi

Answering the question posed in the article, "As of 2002, the record is held by Yasumasa Kanada of Tokyo University at 1,241,100,000,000 digits. That result was never printed out: can you figure out why not?"

An ordinary printed page can hold about 5,000 digits.

To print 1,241,100,000,000 digits would require 248,220,000 pages, or 496,440 reams of paper. A ream of paper is the size of a large book. It would take a building the size of a city library to hold the printed output. Dpbsmith 23:08, 13 January 2007 (EST)

Counting the letters in the phrase "Now I wish I had a drink—alcoholic, of course" Does not help because it gives a wrong answer. it gives 3(.)141315926, it should be 3.1415926... --TimSvendsen 23:54, 15 January 2007 (EST)

• Yikes! I'm going to have to turn in my geek badge. It should be "How I want a drink--alcoholic of course." I was mixing it with "How I wish I could recollect pi easily today." Sorry. Dpbsmith 13:16, 16 January 2007 (EST)

So I'm assuming by the change back to the old version, my revision was no good. An explanation why would be nice, though. ColinR 21:09, 12 March 2007 (EDT)

Groan

What was I thinking here? [1]

113 divided into 355 like this:

      3.14156.....
    ---------
113|355.00000

I had 1/pi by mistake - not even an approximation, more like an abomination. --Ed Poor 23:44, 28 March 2007 (EDT)

I like Pi

Pi R Squared? No they're not, Pie are round. Brownies are square. Human 22:07, 20 April 2007 (EDT)

LOL. --Ed Poor ^Talk 09:08, 11 March 2008 (EDT)

22/7

Besides the fact that "Pi is exactly 3!", 22/7 is also a repeating decimal. Pi is also known as Archimedes' constant, Ludolphine, and Ludolph's Number. Ludolph van Ceulen (Germany) spent a great deal of time calculating digits of pi. The number is engraved on his tombstone. If I were to get buried, I would have all the digits I memorized engraved on it, but I want to get cremated instead. Fuzzy 10:16, 11 March 2008 (EDT)

It is not true that Pi is exactly 3. What is your suggestion to improve the article? --Ed Poor ^Talk 10:31, 11 March 2008 (EDT)

I haven't said anything about my beliefs, let's just leave my life out of this, eh? And, with you saying that pi=3, are you suggesting CP completely rewrites this article? Fuzzy 10:39, 11 March 2008 (EDT)

If you are not claiming that pi = 3, then that makes two of us. :-)

I've made a few updates to the article, primarily about scriptural references and historical estimates. --Ed Poor ^Talk 12:41, 11 March 2008 (EDT)

Is the Bible wrong about pi?

In the ancient world, measurements were not given as exact as they are today, and that was generally considered acceptable. http://www.tektonics.org/lp/piwrong.html DanH 01:22, 10 March 2008 (EDT)

Who said it was wrong? Sloppy ancients aren't nessecarily wrong ancients. Barikada 01:25, 10 March 2008 (EDT)

So, can I reinsert the Bibical perspective? Barikada 17:15, 10 March 2008 (EDT)

It's not relevant simply to note that the Bible happens to approximate it in passing. However, many use it as an argument to show that the Bible is errant, and that's what I surmise may have been the purpose for its inclusion DanH 17:35, 10 March 2008 (EDT)

Wait. The Bible's interpretation of Pi is not relevant to Pi? What? Look, friend, the Bible is always relevant. Barikada 18:14, 10 March 2008 (EDT)

You admit you're an atheist on your user page. Why are you so interested in inserting this in there? DanH 18:15, 10 March 2008 (EDT)

I admit I'm an atheist-- You say it like it's a bad thing. I'm not trying to stat a fight, Dan, I just figure that, as a wiki with a majority of users that are Christian, it would be good to include the Biblical perspective on matters where it has spoken, as is done in shrimp. Barikada 18:18, 10 March 2008 (EDT)

I didn't realize that was still in shrimp. Anyways, as the article posted above explains, the numbers were not meant to be exact, and the circumference and diameter may have been given as approximate estimates, but pi wasn't a concept that most people knew about or cared about. The Bible wasn't meaning to comment on pi at that point, only at the relevant calculations. DanH 18:24, 10 March 2008 (EDT)

That's great, Dan. You seem pretty hostile to the Bible. Barikada 20:16, 10 March 2008 (EDT)

I don't see how Dan seems to be "pretty hostile to the Bible". Your insertion was simply wrong, as the Bible is not trying to give a value for pi at all. Besides, the Bible reference which is frequently quoted by bibliosceptics as supposedly representing pi is already in the article, and even that warrants being removed (in that form) in my opinion. Philip J. Rayment 20:47, 10 March 2008 (EDT)

Oh... So anything a skeptic quotes must be purged, then? What is the purpose of the verse if not to show the value of pi? Furthermore, how do you know what the Bible is and is not trying to say, Philip? Barikada 20:48, 10 March 2008 (EDT)

Also, bibliosceptics is A: Spelled wrong and B: a word which would translate as "Skeptical of books." Barikada 20:49, 10 March 2008 (EDT)

Oh, bugger. It seems I didn't notice that the verse was already quoted in the History section. Barikada 20:51, 10 March 2008 (EDT)

I didn't say that anything a sceptic quotes should be purged.

What's the purpose if not to show the value of pi? To describe the object's size, genius!

What is incorrect about the spelling of "bibliosceptics"? Yes, the word could mean "sceptical of books", but as "Bible" means "book", it's appropriate to use it to mean "sceptical of the Bible".

Philip J. Rayment 21:03, 10 March 2008 (EDT)

"Besides, the Bible reference which is frequently quoted by bibliosceptics as supposedly representing pi is already in the article, and even that warrants being removed (in that form) in my opinion." That's exactly what you said, Philip!

Then why not describe it correctly?

Skeptics. With a K. Also: Yes. I know it means book. Your use of faux Latin does not make you smarter. Barikada 21:13, 10 March 2008 (EDT)

That quote of mine does not indicate that anything a sceptic quotes should be purged, and neither does it say that that bit should be removed because it's something a sceptic quotes.

Aussies traditionally spell "sceptic" with a "c", hence my use of "bibliosceptic" rather than "biblioskeptic".

Philip J. Rayment 22:12, 10 March 2008 (EDT)

A fourth consecutive edit, because a thought occurs. How can we be sure that man's measurements are correct in this case but the Bible is not? Furthermore, if the Bible is wrong here, how can we logically accept that everything else is exact-- IE, the age of the Earth? Barikada 20:56, 10 March 2008 (EDT)

What reason is there to think that the Bible's measurements are incorrect? The logic of your question is valid, but the premise (that the Bible is incorrect) is not. Philip J. Rayment 21:05, 10 March 2008 (EDT)

Well, if it's ten cubits from one side to the other, it should be 31 all around, if we're rounding. Barikada 21:13, 10 March 2008 (EDT)

What if it was actually 9.7 cubits (rounded to 10) from one side to the other? Philip J. Rayment 22:12, 10 March 2008 (EDT)

Then the measurement given is, quite simply, wrong. Barikada 23:44, 11 March 2008 (EDT)

Huh? Okay, I'll have to spell it out for you. If (and this is not the only possible explanation) the actual diameter was 9.7 cubits, then the actual radius would be 30.47 cubits. If both of those figures are rounded to the nearest cubit, then the diameter would be listed as 10 cubits and the circumference would be listed as 30 cubits. And guess what! That's what the Bible lists them as! So if this is correct (and it doesn't have to be exactly that: it could be 9.6 cubits for example), then the Bible is perfectly accurate! ("Accurate" is a different thing to "precise", as Ed mentions below.) If you still aren't convinced, have a look at the links in the External Links section of the article, particularly the Math Forum one. In fact, don't reply here unless you first read the three links. Philip J. Rayment 02:03, 12 March 2008 (EDT)

Yes. Rounding. I get it. It's impercise. If I say Ed is six feet tall, I'm wrong because he's not. If I say he's about six feet tall, I'm right, because he's just over six feet tall. Is that so hard to understand, Philip? Barikada 10:06, 12 March 2008 (EDT)

Alright. Scanned through the links. I get it-- God couldn't be arsed to tell the lowly Earthers a more prescise number. Barikada 17:51, 12 March 2008 (EDT)

You've earned yourself another block for that arrogant response.

If Ed is 6 feet, 3.02 inches tall, would you refer to him as "about 6'3" tall"? The articles said nothing about God not telling us a more precise number. The first link points out that their measurements would not be that precise to start with. In this case, they are not rounding, but simply measuring with a course measuring device. The second reference pointed out that it was common to round numbers in those times. Insisting on using the word "about" is really a case of you expecting people from 3000 years ago to follow your conventions. It doesn't mean that they got anything wrong. The third reference pointed out the following:

• "...in the absence of an explicit indication of precision, the absence of a tenths digit implies that the figure is accurate to the nearest 1 cubit...". So the measurements were accurate to within the implied level of precision!
• "Every measurement we ever make is an approximation.". So do you preface every measurement with "about"? (That's the point of my question above about Ed being 6'3.02" tall.) Absence of the word "about" does not mean that the measurement is "wrong".

You acknowledged none of those points in your response, instead making a silly comment about God. It's clear that you simply want to argue a point that has been thoroughly refuted, and you've stopped doing so civilly. Hence your block. Learn from it.

Philip J. Rayment 21:55, 12 March 2008 (EDT)

You're not wrong to call me six feet tall; I don't mind losing 3 inches in the interest of smooth prose. Just don't call me two meters tall! --Ed Poor ^Talk 18:50, 12 March 2008 (EDT)

That's what the "about" is for-- it indicates impercision. Most useful article ever, by the way. Barikada 18:59, 12 March 2008 (EDT)

I took a few science courses in high school and college. You might be interested to learn about the difference between "accuracy" and "precision". (I probably should compare and contrast the two ideas in a proposed new article: accuracy and precision.)

Here's how it's relevant to Pi. When the Bible says ten cubits, that is an approximation. Scientists would say the measurement is being given to "one significant figure". It really could be anything between 9 and 11 cubits, and it still wouldn't be wrong, because it's only an approximation, like saying that Ed Poor is six feet tall (I'm 6'3" in bare feet).

The ratio between the diameter of a wheel and its circumference is, roughly, three. And if you drew a circle on the ground, with a diameter of 10 cubits, you would pace off 30 cubits when you walked around the circle. Pacing is not a very precise measurement, but it's good enough for some cases. --Ed Poor ^Talk 09:01, 11 March 2008 (EDT)

"It really could be anything between 9 and 11 cubits...": 9.5 and 10.5 actually. Philip J. Rayment 09:06, 11 March 2008 (EDT)

Anyway, you're being too patient with a time-waster. Liberals l-o-v-e to change the subject, with distractions like the supposedly preferable spelling of sceptic. I'm sceptical of this fella's motives, and I've left a note at his talk page. --Ed Poor ^Talk 09:13, 11 March 2008 (EDT)

I would actually like him to answer my last question above, though. Philip J. Rayment 09:43, 11 March 2008 (EDT)

Ed: You'll get a response in the appropriate place momentarily, don't worry.

Philip J. Rayment: So you have wished it, so it shall be. Response is above. Barikada 23:44, 11 March 2008 (EDT)

The Bible does not provide a value for pi, so the following statement is misleading at best:

The Qur'an also defines Pi as 3.(al-Sûra aleph bei).

Use of the word "also" implies that the Bible has provided a definition. The story about the ten cubits does not define pi. It merely gives a diameter and a radius of something presumed to be circular. (A circumference of thirty is consistent with a diameter of ten, with a precision of one significant digit.)

In any case, I'd like to see the exact words of an English translation of any Koran passage related to circle math before approving any claim as damaging as "defines Pi as 3." --Ed Poor ^Talk 11:53, 11 March 2008 (EDT)

Over the years, I've found this to be one of the sillier arguments against the Bible. I've found that those who push it don't believe it, but only do so to try to force in a 'gotcha' that they themselves know isn't the case, but nevertheless they draw enjoyment from trying to act like it is anyway. Learn together 18:48, 28 March 2008 (EDT)

I do not like the "Pi in the Bible" section...

...for many reasons. First, the title is misleading, as the text points out. There is no pi in the Bible (only unleaven bread--just kidding!), nor does the Bible make any attempt to define pi or e or or any other mathematical or physical constant. Second, I think the subject is out of place in an article about mathematics. Perhaps it should be a minor section in an apologetics-related article. Or be omitted entirely, as it is not really a serious criticism, but more a "baby apologetics" thing that appeals to unsophisticated Bible skeptics.

Thirdly, while I appreciate that someone has done the work of gathering the arguments in one place, the wording could be better. It says "Critics claim this, but they are making the following assumptions". Better to say "Critics say this but they are wrong for these reasons." You do not know what someone else's assumptions are.

Fourthly, a minor point. If you opt to keep this section, you might point out that when critics complain that the Bible rounds the circumference to a multiple of ten instead of something more precise (say, 31.4 cubits), they are being inconsistent, because that number is also imprecise. Because pi is irrational, there is no number that could be contained (in a finite Bible) that could give the measurement exactly. What the baby skeptics are doing here is setting an impossible condition for precision, then saying that if the Bible is imprecise it is not inerrant (another big leap in logic), and hoping that no one will notice the flaws in their reasoning.

—The preceding unsigned comment was added by Ga ohoyt (talk)

I wasn't happy with the title either (and I wrote it!), but I wasn't sure what else to have. The next best think I could think of was to put pi in quote marks: "Pi" in the Bible.

I don't think the article is particularly out of place. The article is about pi specifically (not just "mathematics"), and this section is about pi, or at least about a claim made about pi. It is not a serious criticism in the sense of having even a shred of validity, but it is something that is often claimed by bible critics. The Skeptics Annotated Bible mentions it, for example.

As for the mention of assumptions, no, you don't need to know what assumptions they are consciously making; there are certain assumptions inherent in the argument, which is all that the comment is saying. That is, they must be making these assumptions, even if subconsciously. That's not to say that the wording can't be altered to something better, but I do think it's acceptable as it is.

There were a couple of other problems with the claim that I thought of mentioning, but the section was large enough already and the others were in a sense variations on the ones already mentioned, so I thought that was enough. Yes, they often claim that the value is "incorrect", but then are unable to give the "correct" value themselves (because it has an infinite number of digits). And that would be a good thing to point out if the Bible was actually claiming to give a value for pi, but as it's not, it seemed a little bit unnecessary.

Philip J. Rayment 21:48, 13 March 2008 (EDT)

Better now? Ga ohoyt 20:49, 14 March 2008 (EDT)

I'm not sure (but I don't think it's worse). I don't think it's appropriate to have a question for a heading, and neither do I think it's appropriate for the heading to be part of the flow of the text, as is now the case, because the first sentence of the section doesn't make sense without the heading. A heading should give an idea of what the section is about, not be part of the section, if you're following me. Also, the claim is not (normally) explicitly made that the Bible defines pi, as indicated by the heading. Rather, that claim is implicit in the explicit claim that the Bible has an incorrect value for pi. Philip J. Rayment 01:19, 15 March 2008 (EDT)

I think the section is necessary because we do periodically hear this canard about Pi, and the encyclopedia should give the reader the information he needs to respond to it. However, I think the article's response is insufficiently dismissive.

I would simply say that the numbers in the Biblical passage are correct, to their given precision. Hence there is no controversy. Likewise, if an encyclopedia gives the radius and circumference of the Earth to the nearest thousand feet, the encyclopedia is not "wrong about Pi," and nobody would seriously say it was. It seems that only in the case of the Bible are critics so impassioned as to buy such a dopey argument.

Also, I think it is too weak to say it was "common at the time to round numbers." It is common all the time to give measurements like this, and to do so without any conscious or explicit rounding. The way these bullet points are worded, they give the impression that the values D=10 and C=30 need to be explained by some hypothetical act: maybe someone rounded a measurement, maybe they measured different parts of the rim, etc. But D=10 and C=30 does not need any of these explanations because, as I said, they are correct to their given precision, and there is no discrepancy that needs to be explained. I'd just remove them, lest they contribute to the sense of false controversy.--NgSmith

Question on the Bible reference

Were decimals and fractions even in use in the Holy Land at the time 1 Kings was written? Jinxmchue 23:26, 4 April 2008 (EDT)

Decimals, no, I think. Fractions, yes, to some extent, I think. Philip J. Rayment 04:39, 5 April 2008 (EDT)

Pi contains pi

The infinite length of ostensibly random decimal points in means that it contains the equivalent of every book ever written, every birthday, and every other number.

That is quite a misleading statement: Pi (most probably) contains any finite sequence of numbers, therefore any book or birthday date can be "found", e.g., encoded as ascii.

But saying that pi contains "every other number" implies that it contains every number like pi, i.e., every real number. That is obviously wrong. --AugustO (talk) 08:42, July 11, 2021 (EDT)

"Obviously wrong"??? Here is my proof by induction:

1. pi contains pi as one significant digit in a finite representation ("3": 3.141592653....)

2. assume pi contains pi as n significant digits in a finite representation of pi. Pi must also contain pi as n+1 significant digits as the number of digits of pi is stretched to infinity.

Q.E.D.--Andy Schlafly (talk) 13:06, July 29, 2021 (EDT)

Could you explain what you mean by "pi contains pi" exactly? Usually, when looking for birthdays, you would look for a consecutive string of six numbers. And mathematicians are certain that you could find the text of "Hamlet" if you take π mod 26 as a unbroken string. That seems to be different from your idea to find pi... --AugustO (talk) 15:25, July 29, 2021 (EDT)

Not different at all. "Pi contains pi" means what it says: the full pi within pi. Infinity denial appears to be an obstacle here.--Andy Schlafly (talk) 16:38, July 29, 2021 (EDT)

For clarification: π containing π means that there is a consecutive sequence of digits in π (not starting from the first one) which equals π? --AugustO (talk) 17:07, July 29, 2021 (EDT)

Right, as I proved above.--Andy Schlafly (talk) 17:13, July 29, 2021 (EDT)

Sorry for being a little bit thick (or nitpicking) - perhaps I have difficulties because English isn't my first language... OTOH: mathematics is universal!

You are saying that there is a infinite and unbroken sequence of digits in the representation of π (not starting with the first significant digit) equal to π ?

--AugustO (talk) 17:34, July 29, 2021 (EDT)

Yes. Repeatedly asking for clarification of something that is clear could be the result of denial, in this case infinity denial. I don't think the disconnect has anything to do with communication in English!--Andy Schlafly (talk) 22:59, July 29, 2021 (EDT)

As an uninformed, disinterested bystander, I don't see how infinity can be defined by any limited, confined, or known values. Infinity may contain xⁿ number of dimensions, for all we know. How is this so hard to comprehend for people who theorize about life on other planets? RobS^{Free Kyle!} 23:09, July 29, 2021 (EDT)

Doing math in a natural language is sometimes difficult. Luckily, we can get rid of ambiguities by trying to formalize statements.I hope we can agree on the following:

If x₀.x₁x₂x₃x₄x₅...... is the digital expansion of π, then a "infinite and unbroken sequence of digits in the representation of π (not starting with the first significant digit) equal to π" is given by x_nx_n+1x_n+2x_n+3x_n+4x_n+5......, with x_n=3, x_n+1=1, x_n+2= 4, x_n+3=1, and so on and n being a natural number

Thank you for your patience! --AugustO (talk) 01:38, July 30, 2021 (EDT)

Yes, that's right. The aspect of infinity illustrated by the observation that pi contains pi is similar to several of the miracles and parables in the New Testament.--Andy Schlafly (talk) 13:10, July 30, 2021 (EDT)

From your "induction proof", I got the impression that you were looking for increasingly long strings resembling the leading digits of π - I looked up the first few for you:

x9x10	=	35
x137x138x139	=	317
x2120x2121x2122x2123	=	3142
x3496x3497x3498x3499x3450	=	31412
x88008x88009x88010x88011x88012x88013	=	314151
x146451x146452x146453x146454x146455x146456x146457x146458	=	3141597
x25198140x25198141x25198142x25198143x25198144x25198145x25198146x251981407x25198148	=	31415921

But this does not imply that the whole digital representation of π can be found as a consecutive string in π again. In fact, that is impossible.

Yours statement is like saying that as 1, 11, 111, 1111, 11.111, 111.111 and so on are natural numbers, an infinite string of 1s is a natural number, too: And I hope we can agree that this is a false statement. --AugustO (talk) 17:41, July 30, 2021 (EDT)

Your superb examples demonstrate that if true for "n" significant digits, then one can be found later having "n+1" significant digits. This reinforces the proof by induction. I don't see any support for your assertion "that is impossible." I also don't see any connection to your hypothesis about whether an infinite string of 1s is a "natural number," which is simply a matter of definition.--Andy Schlafly (talk) 21:30, July 30, 2021 (EDT)

• Your superb examples demonstrate that if true for "n" significant digits, then one can be found later having "n+1" significant digits. Thanks! But a few examples make no proof.
• This reinforces the proof by induction. No. It does not. As no one has proofed that π is a normal number, your "proof by induction" is on shaky grounds.
• I don't see any support for your assertion "that is impossible." I put it at Talk:Conservapedia insights#Proof that π does not contain π: - it is somewhat of an overkill:

π is given as a digital expansion x0.x1x2x3x4x5... "finding π in π" means that there is an index n such that π starts all over again at xn If π starts again at n, then x0 = xn = 3, x1 = xn+1 = 1, x2 = xn+2 = 4, x3 = xn+3 = 1 and so on. "And so on" means that xk = xk+n for each natural number k, i.e.,. k ∈ N0. What happens if k equals n? What is the value of xn + n? According to the step above, xn + n =xn. But xn=x0=3 ! So, xn + n = xn=x0=3 That's true for all multiples of n: if w ∈ N0, then xw n = x(w-1) n = .... = x2 n = xn = x0 = 3. What about xw n +k ( 0 ≤ k < n )? Again, xw n +k = x(w-1) n +k = x(w-2) n +k = x2 n +k = xn +k = xk So, for every natural number w and every number k with 0 ≤ k < n we have: xw n +k = xk. That makes π periodic, the length of the period is n. Therefore, π can be written as x0x1x2x3...xn-1 / (10n-1 -1) . But this is a rational number, and we know that π is irrational. We have a classical contradiction: As our result is wrong, our assumption that π is contained in π has to be wrong.

• I also don't see any connection to your hypothesis about whether an infinite string of 1s is a "natural number," which is simply a matter of definition. In general, infinity is a difficult concept. But the simplest form of infinity is being "countably infinite". You should make yourself familiar with this concept. Then you would recognize that there is a difference between the statements:

1. a sequence contains a countably infinite number of finite sub-sequences with a certain property and
2. a sequence contains a countably infinite sub-sequence with a certain property

The first statement does not imply the second one. --AugustO (talk) 17:44, July 31, 2021 (EDT)

Your proposed proof has the fallacy of assuming a termination on an infinite sequence (and thus periodicity). There is no such termination.

Your criticism of my proof by induction is also flawed. Do you really think that your examples for n and n+1 will stop existing in the infinite sequence of digits for pi, at some large n? Your position essentially denies the extent of infinity.

Infinity has no such limit. Embrace its vastness and make it work for you. It can be enormously beneficial at a personal level for someone's outlook, and not something to be resisted through infinity denial.--Andy Schlafly (talk) 23:25, July 31, 2021 (EDT)

• "Your proposed proof has the fallacy of assuming a termination on an infinite sequence (and thus periodicity). There is no such termination." That sounds impressive. The proof does not assume "a termination on an infinite sequence" - whatever you mean by this.
• "Your criticism of my proof by induction is also flawed." I have been reluctant to address what you call your "proof by induction" - there is no way to do this charitably. But you forced my hand:

Andrew Schlafly's "Proof by Induction"

π contains π as one significant digit in a finite representation ("3": 3.141592653....)

That's your base case: as π does not equal 3, the sentence "π contains π as one significant digit" is wrong on face value. But, I assume you wanted to say something like "π contains a approximation of π of length 1." So, well done, I'll give you that. Now for the two parts of the induction step:

assume π contains π as n significant digits in a finite representation of π

again, your induction hypothesis is okay: I'd use the phrase "approximation of π of length n", but let's not quibble.

π must also contain π as n+1 significant digits as the number of digits of π is stretched to infinity

What? Why should this be true? Mathematicians have not proofed yet that π is a normal number! You can easily construct a irrational number which contains an approximation of π of length 1010,000, but no approximation of length 1010,000 + 1 . Perhaps God constructed π this way - just to teach mathematicians a little humility. No one knows yet.

But even if your conclusion was true, you would have proofed only that π contains approximations of every imaginable finite length - not of infinite length. That is the same principle which allows you to count to every number, but never reach infinity.

Q.E.D.

Yeah, that's funny.

Andy, I know that you will not be convinced by my arguments (even if you have read them) - you never are. But while getting something wrong in classical Greek makes you look uneducated to a very small minority of readers, being wrong when it comes to the concept of countable infinity makes you look stupid in the eyes of quite a bigger audience.

But therein lies a chance: I assume that you have no one in your circle of friends with whom you could discuss Koine, but I hope that there are mathematically educated persons whom you know: perhaps a high-school teacher, a mathematician (even a student will do) or a physicist, or someone else with comparable background? Ask them: get their help.

Seriously, yours AugustO (talk) 17:06, August 1, 2021 (EDT)

Your infinity denial is illogical. I urge you to welcome and embrace infinity (yes, by implication eternity), and use it for your own benefit. I want you to realize all the happiness and glory it provides.--Andy Schlafly (talk) 16:52, August 2, 2021 (EDT)

Are you still talking about mathematics? --AugustO (talk) 17:00, August 2, 2021 (EDT)

"assume pi contains pi as n significant digits in a finite representation of pi. Pi must also contain pi as n+1 significant digits" - so pi (assuming it's a normal number, as Augusto said) contains any truncated version of pi of any finite length (no matter how many zillions of digits). An infinite number of each truncation. It would also imply that any finite string of digits of pi would be replicated an infinite number of times elsewhere in the string of digits.

"as the number of digits of pi is stretched to infinity." Is it necessary that the pi within pi start at a digit infinitely far from the first digit? That would get around the periodicity issue.

The mathstack discussion: https://math.stackexchange.com/questions/1608060/does-pi-contain-itself

I kind of like the idea of two points on a line being infinitely far from each other, with a third halfway in between, but I don't think that's part of the current standard set of axioms.

We're ignoring the decimal point, right? There's only one of those. Anyway, this is a pretty interesting discussion. AlChesapeake

Right, this is ignoring the decimal point. I like your insight that "pi within pi [would] start at a digit infinitely far from the first digit." I think you're right about that, to get around the periodicity issue, and I'll add that now.--Andy Schlafly (talk) 20:59, September 2, 2021 (EDT)

I am at a loss concerning the proof by induction though - if we start at one digit, then to two, adding one repeatedly, that number will still be an integer, a real number, which (as stated in infinity) cannot be infinity. No matter how large it gets, it's still a finite number. This proves it for all integers n, but infinity isn't in the set of integers. It's beyond! ha ha (that's my attempt at levity) AlChesapeake September 4, 2021

So pi is in pi for any large representation of pi, and that remains true as pi approaches infinity, right? This asymptotic approach of a subset of pi to pi itself is essentially the same as saying pi contains pi, right?--Andy Schlafly (talk) 16:44, September 4, 2021 (EDT)

The book I'm reading (Charles Pinter's A Book of Abstract Algebra) seems to dodge the question - it has a section on inductive proofs, but it just starts with using integers and never mentions infinity. But the digits are countable, and go on for infinity, so they should be countably infinite - you should be able to match each digit to a digit in the countably infinite set of natural numbers, so that makes sense.

I was trying to avoid the term "subset" as by axiom, a set can't contain itself. But I wasn't thinking of this as a set anyway, as there are no duplicates in a set, so the set of all digits in pi would just be the finite {1,2,3,4,5,6,7,8,9,0} after removing duplicates.--AlChesapeake 20:22, September 4, 2021 (EDT)

The sentence in the article has been changed to

Simply stated, Pi contains pi, beginning an infinite number of digits into it (which avoids the periodicity problem).

Let's rewrite this as:

1. pi contains pi after an infinite number of digits into it
2. pi will repeat itself after an infinite number of digits into it
3. pi will repeat itself after an infinite sequence of pi digits
4. an infinite sequence = a sequence that doesn't finish = a sequence without an end = an endless sequence
5. pi will repeat itself after an endless sequence of pi digits
6. pi will not repeat itself before the end of an endless sequence of pi digits
7. an endless sequence has no end
8. pi will not repeat itself
9. pi does NOT contain pi (except for the trivial solution at offset zero)

Please tell me at which line you stop agreeing with this reasoning, so we can expand this further. Blavek (talk) 19:19, September 4, 2021 (EDT)

Reply in bold:

1. pi contains pi after an infinite number of digits into it - YES
2. pi will repeat itself after an infinite number of digits into it - YES
3. pi will repeat itself after an infinite sequence of pi digits - YES
4. an infinite sequence = a sequence that doesn't finish = a sequence without an end = an endless sequence - YES
5. pi will repeat itself after an endless sequence of pi digits - YES
6. pi will not repeat itself before the end of an endless sequence of pi digits - NOT SURE ABOUT THIS.
7. an endless sequence has no end - YES
8. pi will not repeat itself - NO. A NON SEQUITUR
9. pi does NOT contain pi (except for the trivial solution at offset zero) - NO. A NON SEQUITUR

The flaw in your approach is the denial of the existence of an infinite sequence within an infinite sequence. For example, change pi to a set of ordered numbers and then insert pi into that set of numbers.--Andy Schlafly (talk) 19:59, September 4, 2021 (EDT)

To clarify #6: you can either add something after the end, or before the end of a sequence. This is just restating #5 in a different way. Also, it has already been proved that if you repeat a sequence at a finite position, you end with up with a rational number.

The sentence #9 is a direct result from #8 which is itself a result from #6: you can't add digits after the end of something that has no end.

Your remark about a set of ordered numbers is not clear: did you mean natural numbers, real numbers, digits? And how do you insert pi into that set? Blavek (talk) 22:07, September 4, 2021 (EDT)

I think you're making some implicit assumptions about infinity that restrain its power and scope. Infinity can be an infinite sequence of subseries which are themselves of infinite length. My suggestion about sets (which I meant to refer to digits) illustrates that.

By view pi as merely a sequence of digits that stretches on and on does not really capture all of pi's infinity. Infinity is not merely without end. It is also without enumeration. If pi does not repeat itself until after an infinite series of digits, then there is no problem with it becoming a pattern that would render it a rational number, which we know it is not.

Thanks for your comments about this, however, which is helping me clarify my thinking about it!--Andy Schlafly (talk) 22:50, September 4, 2021 (EDT)

The infinite number of digits in the decimal expansion of pi is a countable infinity (aleph₀), the infinity you are talking about is the uncountable infinity of the real numbers (aleph₁). There is an infinite (pun intended) difference between the two. Blavek (talk) 00:12, September 5, 2021 (EDT)

Appreciate the humor! You're right with your examples, but pi is a real number and its decimal expansion is simply an approximation. I don't think "without end" or "after its end" has any real meaning, pun intended!--Andy Schlafly (talk) 00:29, September 5, 2021 (EDT)

Linking to this section from the article

Andy, do you really think that it is a good idea to link to the above section on a talk-page from the main article on π? And please, read the discussion! (ups, that was the second sentence of this paragraph - you probably already started skipping...) --AugustO (talk) 05:23, August 3, 2021 (EDT)