I believe so. It is not periodic while it is transcendental. Maybe that's enough to conclude.I'd like to know if all natural numbers can be found in some part of the decimal expansion of pi.
Hi all,
I'd like to know if all natural numbers can be found in some part of the decimal expansion of pi.
For example in 3.141592 we can find 14,15,92,1592.
The question is a little weaker than the concept of normal numbers, which I heard it's not known if pi is such. So If anyone ever heard about it, please share with us.
Regards,
It is not enough. The number is known to be trancendental. Do you thing its decimal expansion contains the number ? And yet it is bound to contain the integer somewhere.Originally Posted by arbolis:
I believe so. It is not periodic while it is transcendental. Maybe that's enough to conclude.
How confident are you that the decimal expansion of contains the integer somewhere? Very confident? Then I have a used car that you might be interested in ...
But what if I create a rational number like:I believe it is equivalent to asking whether or not pi is a "normal" number, which is still unproven....
0. + 1 + 2 + 2 + 3 + 3 + 3 + ... + + ...
where sum operation denotes concatenation.
It contains all natural numbers, but is that a "normal" number?
Ok, good to know and good point. We cannot conclude.
However I'm confident (by intuition now, I'm not affirming) that the number appears somewhere in the decimals... if the digits are really "randomly" distributed (I'm not sure I making sense here) then should appear.
I find this article to be interesting : Infinite monkey theorem - Wikipedia, the free encyclopedia.