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

I think this argument should hold water.

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Guest Message by DevFuse

Started by k-man, May 15 2014 05:30 PM

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

I think this argument should hold water.

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8 replies to this topic

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...?

Posted 16 May 2014 - 08:53 AM

Spoiler for first thoughts

- Bertrand Russell

Posted 20 May 2014 - 03:01 PM

Any other thoughts?

Spoiler for Conjecture

Posted 20 May 2014 - 04:20 PM

Spoiler for Isnt that

- Bertrand Russell

Posted 20 May 2014 - 04:31 PM

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

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.

- Bertrand Russell

Posted 21 May 2014 - 06:43 AM Best Answer

I think this argument should hold water.

Spoiler for

Posted 21 May 2014 - 07:14 AM

I think this argument should hold water.

Spoiler for

Agree.

- Bertrand Russell

Posted 21 May 2014 - 05:02 PM

Nice explanation, plasmid. Marking as solved.

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