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another very long task


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12 replies to this topic

#1 phil1882

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Posted 12 August 2012 - 06:23 AM

let heads be 1 and tails be 0. can you flip a coin enough times to form an irrational number?
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#2 bushindo

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Posted 12 August 2012 - 04:10 PM

let heads be 1 and tails be 0. can you flip a coin enough times to form an irrational number?


This puzzle statement may be undercontrained,

Spoiler for it seems to be

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#3 superprismatic

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Posted 12 August 2012 - 04:59 PM

Spoiler for ....OR.....

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#4 phil1882

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Posted 12 August 2012 - 08:10 PM

okay maybe some clarification is in order.
clearly no finite number of flips will be enough, assuming you're not allowed to apply a function to it.
but can you mathematically flip an infinite number of coins to represent an irrational number?
i guess what I'm asking is, is the digits of a single irrational number countably infinite?
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#5 jim

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Posted 12 August 2012 - 09:44 PM

Any real number can be expressed by a sign, a finite number of binary digits before a binary point, and then a possibly iinfinite and definitely countable number of binary digits after the binary point. 0.1010010001... would be an example of an irrational number in binary where every run of 0"s countains one more 0 than the previous run and is followed by a single 1.
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#6 TheChad08

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Posted 13 August 2012 - 04:15 AM

Spoiler for

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#7 phil1882

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Posted 13 August 2012 - 05:33 PM

I'm very interested in knowing how you get 16 flips for the value pi, since pi is transcendental.
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#8 superprismatic

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Posted 13 August 2012 - 06:16 PM

I'm very interested in knowing how you get 16 flips for the value pi, since pi is transcendental.

Spoiler for I think TheChad means

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#9 bonanova

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Posted 13 August 2012 - 07:00 PM

TheChad: ^_^
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 EventHorizon

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Posted 16 August 2012 - 05:36 AM

okay maybe some clarification is in order.
clearly no finite number of flips will be enough, assuming you're not allowed to apply a function to it.
but can you mathematically flip an infinite number of coins to represent an irrational number?
i guess what I'm asking is, is the digits of a single irrational number countably infinite?

Spoiler for My thoughts on this...

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