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## Main Question or Discussion Point

If pi is infinite and nonrepetive and every number combination is in pi, somewhere, does that mean pi itself is in pi somewhere.. ? (that would make it periodic)

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If pi is infinite and nonrepetive and every number combination is in pi, somewhere, does that mean pi itself is in pi somewhere.. ? (that would make it periodic)

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CompuChip

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Yes, it is, starting at the first digit :)

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jbriggs444

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If pi is "normal in base ten" then that would mean that every _finite_ sequence of decimal digits occurs somewhere in the decimal expansion of pi.If pi is infinite and nonrepetive and every number combination is in pi, somewhere, does that mean pi itself is in pi somewhere.. ? (that would make it periodic)

There can only be countably many non-terminating decimal expansions found in consecutive digits in the decimal expansion of pi -- the one starting at the first digit, the one starting at the second digit, the one starting at the third digit, etc.

Since there are uncountably many non-terminating decimal expansions, it is certain that not all of them appear.

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Is there any proof that every (finite) number combination is in pi?

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http://www.angio.net/pi/bigpi.cgi

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jbriggs444

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It is not known whether pi is normal in base 10.Is there any proof that every (finite) number combination is in pi?

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[itex]\pi[/itex] is not periodic. If it were it would be in [itex]\mathbb{Q}[/itex] which it isn't.

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HallsofIvy

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Interesting but does not answer the question which was about the entire countable string. On the other hand, Edi seems to be under the impression that we could have entire string,

http://www.angio.net/pi/bigpi.cgi

Edi, it is NOT known whether "every number combination is in pi" is true or not.

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Khashishi

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Then (10^n-1)*pi = q

pi = q/(10^n-1)

To find such an n, pi would have to be a rational number, which is isn't.

So, no, pi cannot repeat or contain itself.

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jbriggs444

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As has been pointed out, n=0, q=0 satisfies this criterion. Pi contains itself -- in a trivial sense.You are looking for a number n such that 10^n*pi-pi is an integer. Call this integer q.

YesThen (10^n-1)*pi = q

pi = 0/0 ?pi = q/(10^n-1)

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Khashishi

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you know what I meant.

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CompuChip

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Happy?You are looking for a number n> 0such that 10^n*pi-pi is an integer.

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jbriggs444

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Well, I could be even more picky and take n = 0.1200175... and q = 1.

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Please stop hijacking this thread. We all know what Khashishi meant.Well, I could be even more picky and take n = 0.1200175... and q = 1.

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