Pi is an irrational number. This means that its digits continue indefinitely without ever repeating. Every possible finite combination of digits is therefore contained therein. This would technically include a digital representation of every possible copyrighted work.
Does this constitute prior art?
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Khurram Wadee
in reply to Jonathan Lamothe • • •Bob Jonkman
in reply to Jonathan Lamothe • • •I'll bite, but not about the IP part.
Just because an irrational number's digits continue indefinitely without ever repeating, does that necessarily mean that it contains every arbitrary finite sequence of digits?
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Bob Jonkman
in reply to Bob Jonkman • • •Is there at least one finite sequence of digits that isn't represented in pi? If so, there are probably an infinite set of finite sequences of arbitrary numbers not represented in pi.
*something something* Cantor's infinite set of infinite sets...
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Bob Jonkman
in reply to Bob Jonkman • • •OTOH, if every finite sequence of arbitrary digits is represented in pi, then we should be able to find in pi a representation of, say, Euler's number to any given precision...
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3/3 Enough for now. I don't have the math-fu to know if I'm being rational.
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Jonathan Lamothe
in reply to Bob Jonkman • •soaproot
in reply to Bob Jonkman • • •@bobjonkman No. Consider 1.0100100010000100001..... This is irrational but it doesn't contain any sequence of digits containing digits other than one or zero.
As for the irrational number pi, I think maybe it is unknown whether it contains all sequences of digits, but I don't know where to quickly check that.
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Jonathan Lamothe
in reply to soaproot • •Bob Jonkman reshared this.
Jonathan Lamothe
in reply to Jonathan Lamothe • •@soaproot ...though could it not then be argued that this number contains a binary encoding of all possible sequences?
Edit: actually, not necessarily.
Edit 2: Okay, I see the pattern now. Definitely not.
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