# Mystery about irrational numbers

I'm new here as you can see.

There is a mystery about $\pi$ that I heard before and want to check if its true. They told me that if I convert the digits of $\pi$ in letters eventually I could read the Bible, any book written and even the history of my life! This happens because $\pi$ is irrational and will display all kind of finite combinations if we keep looking its digits.

If that's true then I could use this argument for any irrational.

My question is: Is this true?

-
That is not necessarily the case: math.stackexchange.com/questions/216343/… –  Sam Apr 7 '13 at 15:44
The short answer is: nobody really knows if this is true. You will probably receive definitive answers soon, with references to the latest research findings. Just because a number is irrational doesn't mean all finite combos of digits occur in its decimal expansion. –  Stefan Smith Apr 7 '13 at 15:45
I could change the way i convert numbers in letters in several ways, doing this would be enough to get the "combos" i want? –  diff_math Apr 7 '13 at 15:48
"eventually i could" ... in the more generous sense of the word "eventually". It's not true that every irrational has that property, but you are right in guessing that $\pi$ is not special in this regard. –  leonbloy Apr 7 '13 at 15:48
Sam, this link is really similar to mine. –  diff_math Apr 7 '13 at 15:52

## 2 Answers

It is absolutely false that all irrational numbers have that property.

For example, look at $$0.10110\underbrace{111}0\underbrace{1111}00\underbrace{11111}0\underbrace{111111}\ldots$$ and continue the pattern. That number is irrational and does not have the property described.

Whether $\pi$ is what is called a normal number is actually not known, and that is what you would need.

-
Does normal numbers know the history of our lives? –  diff_math Apr 7 '13 at 15:50
The history of your life would be there, as would many lies about you, and immense amounts of gibberish, but there would be no to predict where the gibberish is and where the meaningful patterns are. Normal actually means that every finite sequence of digits would occur exactly as frequently as every other finite sequence. –  Michael Hardy Apr 7 '13 at 15:52
Is there some chance to exists a ideal number, with no lies, no gibberish? A number telling exact all the facts. –  diff_math Apr 7 '13 at 15:55
If you can write something with no gibberish, you can probably encoded it as a number, and there you've got it. –  Michael Hardy Apr 8 '13 at 0:25

$\pi$ is just another number like $5.243424974950134566032 \dots$, you can use your argument here. Continue your number with number of particles of universe, number of stars, number of pages in bible, number of letters in the bible, and so on. And 'DO NOT STOP DOING SO, if you do the number becomes rational'.

There are another set of numbers which are formed just by two or three numbers in its decimal expansion, take an example :$0.kkk0\underbrace{kkkk}0\underbrace{kkk}000\underbrace{k}0000\underbrace{kk}\ldots$, where $0<k \le 9$. An irrational number is just defined as NOT Rational number. In other means, which can't be expressed in the form $\dfrac{p}{q}$.

When I was reading about $\pi$, I just found this picture, Crazy $\pi$.

-
Original source of the picture: (xkcd.com/10) –  Quincunx Apr 25 '13 at 17:56