Does Pi contain my phone number.

[MrBaggins]

Originally posted by Anunikoba


Once again, I am not debunking quantum theory (as incomplete as it is) as yes, it does work. It is this statement:

"Everything happens, and keeps on recursively happening.

We only perceive one of those realities."

that fails the proof test.

Actually, no... the fundemental principal of Quantum Field Theory and its divergence with General Relativity, is that there are infinities. QC leverages Quantum Field Theory behavior as much as Quantum Mechanics.

[Thue]

Maybe I should correct all the mistakes...

Nah, to much work .

[Adalbertus]

Actually, we don't really know if Pi really is an irrational number, do we?

I've never bothered so much about piology, but there exists a proof that pi is irrational (you can prove such things without checking all decimals), and there exists also a proof that every finite sequence of digits is contained in pi. I don't know where to find the proof, and I'm not so much interested in that topic as to search for it. Sorry.

Btw. If pi were a rational number, the "quadrature of the circle" would be possible, i. e. to geometrically construct a square with the same area as a given circle, using pen, ruler and compasses only. It has been proved to be impossible.

[Adalbertus]

Originally posted by Cesar the Great
say you have a number line from negative infinity to infinity and you made a point for each rational number and each irrational number, the set of points for the rational numbers is A and the set of points for the irrational numbers is B. are there more elements in set A or set B?

You have more elements in set B.

Preliminaries:
First, the mathematician's notion of "has the same number of elements" is perhaps a bit counterintuitive. For sets in general, one talks about the cardinality, #A, of a set A. For finite sets, this is just the familiar number of elements. For infinite sets, you start with mappings. Take two sets A and B, then you can map each element of A to an element of B., in some way. (the familiar functions are examples of mappings, or numbering a set of six eggs is a mapping of the set {1,2,3,4,5,6} to the set of your eggs.)

Then you define mappings, who for each element of A have a unique image in B, as injective. More mathematically: A mapping f:A->B is injective if and only if for each a and b in A holds that if f(a) = f(B) then a=b.
The labelling of the eggs is injective. The sine function is not, as sin (0)= sin(pi), but 0 != pi.

Now back to the cardinalities: One defines for two sets A and B that #A <= #B if there exists an injective mapping f:A->B. This is exactly the way you would try to find out if you have more steaks or more plates. Further one defines #A =#B if #A <= #B and #B <= #A.

If you think a bit over it you will make the stunning discovery that there are as many even numbers as integers (see below for something even stranger). This seems to be odd at first, but there is no better way to define the "number of elements" for infinite sets.

Now we are prepared for infinity. First: There are as many rational numbers as positive integers.
Proof: Denote the set of positive integers by N and of positive rational numbers by Q. We already know that N is a subset of Q, therefore the injective mapping f:N->Q is trivially built. (note, there is no reason to exhaust Q with this mapping).
Then we know that each rational q can be expressed as a fraction n/m. Now set up the following scheme:

1/1 1/2 1/3 1/4 1/5 ....
2/1 2/2 2/3 2/4 2/5 ....
3/1 3/2 3/3 3/4 3/5 .....
4/1 4/2 4/3 4/4 4/5 ....

and so on. This scheme contains all positive rational numbers. Now start in the top left. Label the number 1/1 as 1. Then go down. Label 2/1 as 2. Then go right up, label 1/2 as 3. Go right, find 1/3 as 4. Go left down. 2/2=1/1, so skip this number. Again left down, 3/1 is number 5. And so on.:
_ _
|/ / / /
/ / /
/ / /
|_/

I'm not a good ASCII painter, but I think you see the path. Anyway, you label each of the positive rational numbers with a unique positive integer, so you have also #Q <= #N. The sets thus have the same cardinality, i. e. "number" of elements.

So, now about the positive real numbers, R. Let's assume we have already proven that each decimal number has a unique decimal expansion (except for 1=0.999999... and analogue). Then we assume we have successfully numbered all decimal numbers. Then we write them in a long list

3.1415926.....
2.7182818....
1.2000000....
etc.

Then we take the first number and change the first digit, take the second number, change the second digit, etc.
1.1415926...
2.4182818...
1.2100000...
etc.

and collect the changed digits to a new number, in this case 1.41... This number is clearly a real number and clearly not in our list. Which means there is no injective mapping f:R->N, or in other words #R > #N.

Now, the irrational I numbers are a subset of R only, such that R is the union of Q and I. Now, if I were countable (which means, #I = #N), then we could easily construct an injective mapping from R->N by mapping Q to the even and I to the odd numbers for example. Therefore, #I>#Q. (In fact, one can show, but I don't know, how atm, it's time for bed now, that #I=#R).

An interesting side note: It has been shown that it is impossible to know if there is a set A which fulfills #N < #A < #R.

Good night.

[pchang]

Likely is the wrong word

Originally posted by orange


I'm not saying it 'won't' but I am saying that it's more likely for conner's phone number to appear than it is for 12345678987654321 (repeated a thousand times over) to occur because of the SIZE of the number and repatative nature of the integer.

Look at the definition of an irrational number. Once you understand that, you will understand that likely is not the correct word. Both number DEFINITELY appear in Pi.

The proper word is frequency. Conner's phone number appears more frequently than your number.

Please note that both numbers appear an infinite number of times inside Pi.

[connorkimbro]

"Does Pi contain my phone number?"

the answer is YES

It does. I won't tell you where it's at though. In fact, it contains both my cell phone number AND my regular phone line.

The following web page will search the first 100,000,000 digits of pi and attempt to find a string of numbers that you enter. So, there.

lol

http://www.angio.net/pi/piquery

[Adalbertus]

Look at the definition of an irrational number.

The statement "any finite sequence of digits can be found in the digits of pi" needs an independent proof. It cannot be deduced from the fact that pi is irrational.

The irrational number 1.01001000100001...
with always one 0 more between the 1's naturally cannot contain the number 42. Note, this is a decimal number. There exists also a binary number 1.01001000100001... which is bigger than the decimal number, it is about 1.28326... .


Slowly I begin to understand why a question which simply can be answered "yes" develops in a four page thread.

[KrazyHorse]

Originally posted by connorkimbro
Yeah, but it's not like 10 divided by 3 which gives you an infinite string of 3's. It's always different numbers, and never repeats a pattern.

If you can prove that Pi must contain every possible finite string of digits then I'll give you 10$

*Begins practicing acceptance speech for Fields medal*

[KrazyHorse]

Re: It does

Originally posted by LulThyme
If your phone number is finite in length
then it is contained in Pi's decimals
actually this is true for any irrationnal number's decimals and any phone number of finite length (not just yours )
I even think there are some sites where you can input a string of digits and it looks where in the digits of pi it appears for the first time.
for 7 digits im not sure how efficient sucha site would be though ud have to look

I'm pretty sure this just ain't true.

Actually, I am sure.

The number:

0.10110111011110111110....

is irrational (and I'm pretty sure it's transcendental too), however it does not even contain every possible 1-digit string (doesn't contain digits 2-9).

[KrazyHorse]

Originally posted by Juggernaut
Actually, we don't really know if Pi really is an irrational number, do we?

Since we've never seen the end to it, we can't be sure it doesn't eventually start repeating itself and become, albeit extremely complex, rational.

You can pretty easily prove that Pi is irrational from some of its series expansions (expression as an infinite sum). Proving that it's transcendental is slightly harder, but it's been done.

[KrazyHorse]

Re: Likely is the wrong word

Originally posted by pchang


Look at the definition of an irrational number. Once you understand that, you will understand that likely is not the correct word. Both number DEFINITELY appear in Pi.

The proper word is frequency. Conner's phone number appears more frequently than your number.

Please note that both numbers appear an infinite number of times inside Pi.

Not necessarily true, AFAIK. Definitely not true simply because Pi is irrational.

[SnowFire]

Ugggggggggghhh. I smell lots of horribly false statements.

Interestingly enough, onr of our math-faculty lunches here had the topic "Is Pi normal?" Interesting that word hasn't come up yet, but normal means that for any string of length k in base b, there is 1/(b^k) chance of finding that string in all strings of length k in the decimal expansion. So in base 10, 1/10 of the digits are 2's, 1/10 are 3's, 1/100 of the 2-string patterns are "23," etc.

As KrazyHorse pointed out, proving pi is normal might get you a Fields Medal. But from what we've expanded so far and general evidence, pi at least "seems" random enough to be normal. Also, any random irrational number you choose is irrational (want to generate an irrational number? Roll a 10-sided die over and over again and write it down)- random selection of irrationals will give you probability 1 of picking a normal one, so the odds are on the side of pi being normal as well. The examples given of things like .010010001... are bizarre degenerate cases... which pi might be, but I doubt it myself.

[KrazyHorse]

Probable, but not certain.

Just like I can show you that it's probable that any number you show me is irrational...

[Urban Ranger]

Originally posted by SnowFire
Also, any random irrational number you choose is irrational (want to generate an irrational number? Roll a 10-sided die over and over again and write it down)- random selection of irrationals will give you probability 1 of picking a normal one, so the odds are on the side of pi being rational as well.

You meant normal, yes?

[orange]

Originally posted by connorkimbro
"Does Pi contain my phone number?"

the answer is YES

It does. I won't tell you where it's at though. In fact, it contains both my cell phone number AND my regular phone line.

The following web page will search the first 100,000,000 digits of pi and attempt to find a string of numbers that you enter. So, there.

lol

http://www.angio.net/pi/piquery

The string 302837**** did not occur in the first 100000000 digits of pi after position 0.

not for me