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.
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?
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...
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...
@Bob Jonkman So I've been told. I also took it as a given that the numbers never repeat. I have a mathematical proof for at least the non-repeating part now at least.
@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.
I have a messenger bag that I typically carry around with me. Sometimes things go in there and I forget about them.
Katy was looking for something and discovered that for some reason I had put our marriage certificate in there. The last time I needed the physical certificate was years ago, so it must've been sitting in there and I've just been carrying it around with me unknowingly for quite some time.
I imagine I should probably find a better place for it.
I should probably also go through it to see what else I've put in there and forgotten about.
In what may be the first time in the history of the world that anyone has done this, I just managed to use super glue without getting any on my fingers.
Remastered:
Trapped In Treatment is a new docu-style podcast series from Paris Hilton & Warner Bros. Unscripted TV in Association With Telepictures, and iHe
I've stated before that I'm not the CW police and I'm not going to dictate how others should use them, but if you're looking for a general guideline on when you might consider using them, this seems a reasonable guide:
I find that hlint is a great tool for pointing out where your code can be improved, but sometimes its suggestions are... interesting. Case in point, it just recommended changing
map (\(a, b) -> {- ...stuff... -}) $ zip as bs
to
zipWith (curry (\(a, b) -> {- ...stuff... -})) as bs
In this remastered episode I chat with someone who has experienced The International Society for Krishna Consciousness. Michael gives a deep dive into many type
PSA: If you are in a group and there exists one or more individuals within that group who must not be criticized under any circumstance, you are in a cult.
I would worry an "update" might be an anti-root patch to prevent owners from adding features and higher sampling rates found in much more expensive models
@Spacegoat From what I overheard it sounds like it was a drug bust. They hauled the driver away and eventually towed the car after a bunch of them turned it inside out.
We have to order @Benny's food from the vet because he's on a prescription diet. Tried using their on-line ordering option. We ordered his food a week ago. It just arrived this morning.
@wing Been meaning to give Jellyfin a go ever since you and Hex mentioned it. Finally got around to it. You'll be happy to know that the first video I tested it with was, in fact, Big Buck Bunny.
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?
#Mathstodon
1/
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...
#Mathstodon
2/
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...
#Mathstodon
3/3 Enough for now. I don't have the math-fu to know if I'm being rational.
#BaDumTiss
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.
Jonathan Lamothe likes this.
Bob Jonkman reshared this.
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.
Bob Jonkman reshared this.