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# Probability in Pi

Best Answer plasmid, 21 May 2014 - 06:43 AM

I think this argument should hold water.

Spoiler for

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8 replies to this topic

### #1 k-man

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Posted 15 May 2014 - 05:30 PM

It is a well-known fact that the number pi is an irrational number. This means that its decimal representation is infinitely long.

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664...

What is the probability that pi's decimal representation contains a sequence of digits ...0123456789....?

What is the probability that it contains ...33333333333333333333...?

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### #2 bonanova

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Posted 16 May 2014 - 08:53 AM

Spoiler for first thoughts

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Vidi vici veni.

### #3 k-man

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Posted 20 May 2014 - 03:01 PM

Any other thoughts?

Spoiler for Conjecture

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### #4 bonanova

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Posted 20 May 2014 - 04:20 PM

Spoiler for Isnt that

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### #5 k-man

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Posted 20 May 2014 - 04:31 PM

Maybe it is. I don't know as I've never heard of it before

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### #6 bonanova

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Posted 20 May 2014 - 04:41 PM

I don't know that it applies, although it sounds related. As I recall hearing it, it holds that a system will visit every available state given enough time. A weaker "quasi" ergodic theorem says that a system will visit a finite region around every available state (implying there is a distance function of some type) given enough time.

The resolution of your conjecture may not be covered by either of these.

The resolution may rest on certain conditions being satisfied. It's a zero-times-infinity puzzle that might require either a strong intuition or great mathematical skill to answer. I have some intuition, but it's often wrong. That fact keeps me coming back to this site.

So I wonder whether the decimal expansion for e can occur within the expansion for pi.

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### #7 plasmid

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Posted 21 May 2014 - 06:43 AM   Best Answer

I think this argument should hold water.

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### #8 bonanova

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Posted 21 May 2014 - 07:14 AM

I think this argument should hold water.

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Agree.

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### #9 k-man

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Posted 21 May 2014 - 05:02 PM

Nice explanation, plasmid. Marking as solved.

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