4 ms·

Here is pi, written as a number to infinite precision (from http://davidbau.com/archives/2010/03/14/python_pipy_spigot.html http://davidbau.com/archives/2010/03

Here is pi, written as a number to infinite precision (from http://davidbau.com/archives/2010/03/14/python_pipy_spigot.html http://davidbau.com/archives/2010/03/14/python_pipy_spigot.h... ): def pi_decimal_digits(): q, r, t, j = 1, 180, 60, 2 while True: u, y = 3*(3*j+1)*(3*j+2), (q*(27*j-12)+5*r)//(5*t) yield y q, r, t, j = 10*q*j*(2*j-1), 10*u*(q*(5*j-2)+r-y*t), t*u, j+1 If you mean that pi can't be written as a number to infinite precision using place-value notation (as opposed to a more useful notation like Python) then I agree that only a finite prefix can ever be observed.

mcguire 5y ago
Note that the Python version of pi requires an unbounded amount of memory and, more importantly, an infinite amount of time to produce pi to infinite precision.
- chriswarbo 5y ago
  > Note that the Python version of pi requires an unbounded amount of memory Really? I measure it as exactly 200 bytes (not counting the 4-space indentation that HackerNews requires, and not including a trailing newline) > and, more importantly, an infinite amount of time to produce pi to infinite precision I can see it right now, with infinite precision. If it's taking an infinite amount of time to show up I'd contact your ISP ;)
  - mcguire 5y ago
    Ah, I see where you are going with this. However, I can offer a version which, without loss of generality, gives another 200-to-1 compression (not counting UTF-8 multibytes): π. There it is, in all it's infinite splendor.
- Kranar 5y ago
  Not at all, the reason you may think so is that you're very used to representing numbers using a base 10 number system and in that system it is inherently impossible to represent pi. But if you change how you represent numbers, you can represent pi exactly. What OP did was represent pi using a syntax inspired by a programming language, which is just as valid a number system as any other formal representation as far as correctness goes, although of course as a human I likely would not wish to express most of my use cases involving numbers using a full blown programming language. That said, one can perform all of arithmetic using that system and represent any property of numbers that could be represented otherwise.
mensetmanusman 5y ago
Also, pi = C/d in geometry notation :)
lmm 5y ago
What you've written is not pi, it's a procedure for computing pi. Python expressions are not a notation, they fail basic requirements for a reasonable notation (for example you cannot generally determine whether two Python expressions are equal or not).
- mietek 5y ago
  You may find it interesting to learn that one cannot generally determine whether two real numbers are equal or not: equality on real numbers is undecidable.
  - lmm 5y ago
    I'm well aware. It's also the case that there is no good notation for the real numbers; in particular since any given notation system can only represent countably many distinct entities, almost all real numbers will be are unrepresentable in that notation system. Therefore the notion that the full set of reals actually exists is extremely dubious.

mcguire 5y ago

Note that the Python version of pi requires an unbounded amount of memory and, more importantly, an infinite amount of time to produce pi to infinite precision.

chriswarbo 5y ago
> Note that the Python version of pi requires an unbounded amount of memory Really? I measure it as exactly 200 bytes (not counting the 4-space indentation that HackerNews requires, and not including a trailing newline) > and, more importantly, an infinite amount of time to produce pi to infinite precision I can see it right now, with infinite precision. If it's taking an infinite amount of time to show up I'd contact your ISP ;)
- mcguire 5y ago
  Ah, I see where you are going with this. However, I can offer a version which, without loss of generality, gives another 200-to-1 compression (not counting UTF-8 multibytes): π. There it is, in all it's infinite splendor.
Kranar 5y ago
Not at all, the reason you may think so is that you're very used to representing numbers using a base 10 number system and in that system it is inherently impossible to represent pi. But if you change how you represent numbers, you can represent pi exactly. What OP did was represent pi using a syntax inspired by a programming language, which is just as valid a number system as any other formal representation as far as correctness goes, although of course as a human I likely would not wish to express most of my use cases involving numbers using a full blown programming language. That said, one can perform all of arithmetic using that system and represent any property of numbers that could be represented otherwise.

mensetmanusman 5y ago

Also, pi = C/d in geometry notation :)

lmm 5y ago

What you've written is not pi, it's a procedure for computing pi. Python expressions are not a notation, they fail basic requirements for a reasonable notation (for example you cannot generally determine whether two Python expressions are equal or not).

mietek 5y ago
You may find it interesting to learn that one cannot generally determine whether two real numbers are equal or not: equality on real numbers is undecidable.
- lmm 5y ago
  I'm well aware. It's also the case that there is no good notation for the real numbers; in particular since any given notation system can only represent countably many distinct entities, almost all real numbers will be are unrepresentable in that notation system. Therefore the notion that the full set of reals actually exists is extremely dubious.