Infinitely Print Zeno's Dichotomy Paradox (1/(2^n))

Question

An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders half a beer. The third one orders a fourth of a beer. The bartender stops them, pours two beers and says, "You're all a bunch of idiots."

Reddit

Print the following series for as long as the program runs, with the denominator of each item being multiplied by two each time:

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...

As n approaches infinity, the sum of this sequence approaches 2.

Rules

No, you may not print 2.

You may not print 1/1 as the first item.

You may remove spaces 1+1/2+... or add spaces 1 + 1 / 2 + ... as you need.

You may use newlines instead of spaces as a delimiter due to popular demand.

You may append a . plus a constant number of 0s to the denominator if need be.

"Infinitely" means no unnecessary delays, and for as long as possible limited by the current (variable) system's specs, but not limited by your current language.

Standard loopholes apply.

This is code-golf, so shortest answer in bytes wins.

Regarding the joke, I like the "You guys should know your limits" version better. — March Ho, Commented May 16, 2017 at 13:17
@StephenS Yes, I saw them too, but this one is much clearer and bigger. — Adám, Commented May 16, 2017 at 14:22
@Adám: yep! If the lengths of the denominators weren't changing, then the visual pattern of +1/s would just form a diagonal line. However, the lengths of the denominators is changing linearly (up to rounding): the number of digits of 2^n is about n log(2)/log(10). That linear change translates into a linear change in the relative position of each +1/ with respect to the preceding one, which is the same as a quadratic change in the absolute position. — Greg Martin, Commented May 16, 2017 at 17:02
@QPaysTaxes then you are non-competing - but if multiple people want to post competing C answers, you can compete against each other :) — Stephen, Commented May 16, 2017 at 23:21

Beta Decay · Accepted Answer · 2017-05-16 13:18:18Z

1

Fourier, 20 bytes

1~io(43a1o47ai*2~io)

Try it online!

I think this may only work on Try it Online due to differences in how Python and Javascript handle large numbers.

Explanation Psuedocode:

i = 1
Print i
While i != 0
    Print "+1/"
    i = i * 2
    Print i
End While

edited May 16, 2017 at 13:18

answered May 16, 2017 at 12:55

Beta Decay

23.4k8 gold badges72 silver badges165 bronze badges

\$\begingroup\$ Can you not move the Print i to the start of the While loop? \$\endgroup\$
– Neil
Commented May 16, 2017 at 15:00
\$\begingroup\$ @Neil I could, but it wouldn't say any bytes \$\endgroup\$
– Beta Decay
Commented May 16, 2017 at 15:32
\$\begingroup\$ Oh, I see now, you're not actually printing i. \$\endgroup\$
– Neil
Commented May 16, 2017 at 15:37

Add a comment |

marmeladze · Accepted Answer · 2017-05-16 13:28:34Z

1

Ruby 46 bytes

i=1;loop{print (i<2?"#{i}":"1/#{i}")+"+";i*=2}

any improvement suggestions are welcome -))

answered May 16, 2017 at 13:28

marmeladze

2273 silver badges8 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

1

F#, 39 bytes

let rec f x=printf"%A+1/"x;x*2I|>f
f 1I

Try it online!

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered May 16, 2017 at 14:38

goric

2812 silver badges6 bronze badges

Add a comment |

Robert Hickman · Accepted Answer · 2017-05-16 21:10:59Z

1

Labyrinth, 25 bytes

)
:}!43.4
"     9
*{2.74.

Try it online!

answered May 16, 2017 at 21:10

Robert Hickman

7213 silver badges9 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

1

Common Lisp, 42 bytes

(do((x 1(* x 2)))(())(format t"~a+"(/ x)))

Try it online (TIO will show you partial output)

Explanation

(do ... )          ;looping
((x 1(* x 2))      ;define x as 1 and then in new interation steps 
                   ;as result of 2 * x
(())               ;no ending condition
(format t"~a+"...) ;print argument and "+"
(/ x)              ;divide 1 by x - output is like this: 1, 1/2, 1/4, ...

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered May 17, 2017 at 11:24

user65167

Add a comment |

Jake Taylor · Accepted Answer · 2017-05-17 11:56:06Z

1

PHP, 29 bytes

for($a=.5;$a*=2;)echo"$a+1/";

answered May 17, 2017 at 11:56

Jake Taylor

2011 silver badge4 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

1

Ruby, 24 bytes

a=1;a/=2r while$><<a<<?+

Try it online!

Heavily based on G B's answer. But rationals are fun :V

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered May 18, 2017 at 12:37

Jenkar

2211 silver badge4 bronze badges

Add a comment |

eush77 · Accepted Answer · 2017-05-18 12:50:56Z

1

GNU Make, 45 57 bytes

Using shell:

$(eval 1?=1)$(info $1+1/)$(call $0,$(shell expr $1 \* 2))

Using GMSL (a lot slower, calculates in unary), a complete makefile — 66 bytes:

include gmsl
P=$(info $1+/)$(call P,$(call double,$1))
$(call P,1)

edited May 18, 2017 at 12:50

answered May 17, 2017 at 7:24

eush77

1,3907 silver badges11 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

1

MSX-BASIC, 36 bytes

1?"1+":X=2
2?"1/";X;"+":X=X*2:GOTO2

It works up to 70368744177664, then it starts displaying the values in exponential notation due to the precision limitation of the language, then it overflows at 1e62.

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered May 18, 2017 at 15:49

Konamiman

3511 silver badge5 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

Taxi, 916 bytes

2 is waiting at Starchild Numerology.'1' is waiting at Writer's Depot.Go to Writer's Depot:w 1 r 3 l 2 l.Pickup a passenger going to Post Office.Go to Post Office:n 1 r 2 r 1 l.Go to Starchild Numerology:s 1 r 1 l 1 l 2 l.Pickup a passenger going to Cyclone.Go to Cyclone:e 1 l 2 r.[r]Pickup a passenger going to Trunkers.Pickup a passenger going to Multiplication Station.Go to Trunkers:s 1 l.Go to Multiplication Station:e 1 r 4 l.Pickup a passenger going to Cyclone.Go to Cyclone:s 1 r 2 l 2 r.Pickup a passenger going to Multiplication Station.Pickup a passenger going to The Babelfishery.' + 1/' is waiting at Writer's Depot.Go to Writer's Depot:s.Pickup a passenger going to Post Office.Go to The Babelfishery:n 1 r 2 r 1 r.Pickup a passenger going to Post Office.Go to Fueler Up:n.Go to Post Office:s 1 r 1 l.Go to Trunkers:s 1 r 1 l.Pickup a passenger going to Cyclone.Go to Cyclone:w 2 r.Switch to plan "r".

Try it online! (TIO will output the first 893 terms (up to ~3.3×10²⁶⁸) before cutting it off.)

Ungolfed:

2 is waiting at Starchild Numerology.
'1' is waiting at Writer's Depot.
Go to Writer's Depot: west 1st right 3rd left 2nd left.
Pickup a passenger going to Post Office.
Go to Post Office: north 1st right 2nd right 1st left.
Go to Starchild Numerology: south 1st right 1st left 1st left 2nd left.
Pickup a passenger going to Cyclone.
Go to Cyclone: east 1st left 2nd right.
[r]
Pickup a passenger going to Trunkers.
Pickup a passenger going to Multiplication Station.
Go to Trunkers: south 1st left.
Go to Multiplication Station: east 1st right 4th left.
Pickup a passenger going to Cyclone.
Go to Cyclone: south 1st right 2nd left 2nd right.
Pickup a passenger going to Multiplication Station.
Pickup a passenger going to The Babelfishery.
' + 1/' is waiting at Writer's Depot.
Go to Writer's Depot: south.
Pickup a passenger going to Post Office.
Go to The Babelfishery: north 1st right 2nd right 1st right.
Pickup a passenger going to Post Office.
Go to Fueler Up: north.
Go to Post Office: south 1st right 1st left.
Go to Trunkers: south 1st right 1st left.
Pickup a passenger going to Cyclone.
Go to Cyclone: west 2nd right.
Switch to plan "r".

Explanation:

Pickup the string `1` and print it to stdout to get started.
Pickup the number `2` and duplicate it so we have one to keep around and one to print.
Abuse the truncation function to leave a `2` for later.
(It's en route and has a short name so it saves bytes which is really important in Taxi.)
Go multiply the running total by 2.
(The first time, it's just a `2` so it returns itself. After that, it's 2 times the running total.)
Pickup the string ` + 1/`.
Convert the multiplication result from a number to a string.
Get gas.
Print the string ` + 1/` and the string multiplication result to stdout.
Go pickup that `2` from Trunkers, copy it again, and go back to `[r]`.

The output has trailing zeros on every number: 1 + 1/2.000000 + 1/4.000000 + ... but, per a comment by OP, that's OK so long as it's the same number of zeros every time.

Felipe Nardi Batista · Accepted Answer · 2017-05-18 19:48:17Z

1

Lua 5.1 + BC, 50 bytes

Now works with arbitrary long integers.

I don't usually golf in Lua, so any tips are welcome

i=1::a::print(i,'+1/')i=require"bc".mul(i,2)goto a

edited May 18, 2017 at 19:48

answered May 16, 2017 at 12:53

Felipe Nardi Batista

2,4211 gold badge14 silver badges32 bronze badges

\$\begingroup\$ You can omit some newlines to save bytes. \$\endgroup\$
– Leaky Nun
Commented May 16, 2017 at 12:55
\$\begingroup\$ You can use while 1 do instead. \$\endgroup\$
– Leaky Nun
Commented May 16, 2017 at 12:57
\$\begingroup\$ @LeakyNun that will output garbage in the output when overflow happens \$\endgroup\$
– Felipe Nardi Batista
Commented May 16, 2017 at 12:58
\$\begingroup\$ But then your answer does not print infinitely... \$\endgroup\$
– Leaky Nun
Commented May 16, 2017 at 13:00
\$\begingroup\$ @LeakyNun original spec said thar language limitation could end the execution as well, i'll check \$\endgroup\$
– Felipe Nardi Batista
Commented May 16, 2017 at 13:01

| Show 4 more comments

MickyT · Accepted Answer · 2017-05-18 20:11:37Z

1

Cubix, 26 bytes

oruUroorp"/1+"1>O2uw"wo;;q

A fairly linear program. Push characters /1+ onto the stack, push 1 onto the stack. Start loop, output number, multiply it by 2, push it to the bottom, pop the multipliers, output the characters on the stack and loop.

Try it here

Maps to

      o r u
      U r o
      o r p
" / 1 + " 1 > O 2 u w "
w o ; ; q * . . . . . .
. . . . . . . . . . . .
      . . .
      . . .
      . . .

answered May 18, 2017 at 20:11

MickyT

12.2k2 gold badges26 silver badges48 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

Clojure, 59 bytes

#((fn[n](print(if(= 1M n)1(str 1\/ n))\+)(recur(* n 2)))1M)

A function that prints the fraction, doubles the denominator, then recurses.

(defn zenos-dichotomy-paradox []
  ; Create an anonymous function...
 ((fn [n]
    ; ... that prints the fraction (or just 1 if (= n 1))...
    (print
      (if (= 1M n) 1 (str 1 \/ n))
      \+)
    ; ..., doubles the denominator, then recurses infinitely.
    ; Will not SO since I'm using recur.
    (recur (* n 2)))
   ; Start the recursive function off with a 1. The M makes it a BigInteger so
   ;  I don't get an IntegerOverflow.
  1M))

Outputs

1 +1/2 +1/4 +1/8 +1/16 +1/32 +1/64 +1/128 +1/256 +1/512...

I can make the spacing more consistent at the cost of 2 bytes if necessary.

I tried to be clever and abuse Clojure's built in Ratio number type, but I got an overflow pretty quickly. 1/1 would have been automatically simplified to 1, getting rid of 1 as a special case. It would have been nice.

Razetime · Accepted Answer · 2020-11-11 10:02:52Z

1

Husk, 9 bytes

J'+ms:1İ½

Try it online!

due to a lack of a 0 term, 1 is manually prepended.

answered Nov 11, 2020 at 10:02

Razetime

27.4k3 gold badges29 silver badges72 bronze badges

Add a comment |

Kevin Cruijssen · Accepted Answer · 2020-11-11 14:35:52Z

MathGolf, 9 bytes

ïóoù+1/q∟

Try it online.

Explanation:

        ∟  # Do-while true without popping:
ï          #  Push the 0-based loop index
 ó         #  Pop and push 2 to the power this index
  o        #  Output it with trailing newline (without popping)
   ù+1/    #  Push string "+1/"
       q   #  Pop and push without trailing newline

Unfortunately MathGolf doesn't output implicitly even if it errors when we stop the infinite program, otherwise the o and q would have been unnecessary, because everything on the stack is joined and output implicitly at the end of a (properly terminating) MathGolf program.

Xcali · Accepted Answer · 2021-01-05 03:08:06Z

1

Perl 5 `-Mbigint`, 26 bytes

print 2**$_++,'+1/'while 1

Try it online!

Using bigint means that this could go on forever without turning into a floating point exponential format, given enough time and RAM. TIO gets to about 1/2⁹²² before cutting off due to the 128 KiB output limit.

answered Jan 5, 2021 at 3:08

Xcali

16.2k2 gold badges15 silver badges39 bronze badges

Add a comment |

Razetime · Accepted Answer · 2021-04-30 07:41:43Z

1

Stax, 7 bytes

â─$∩√Öu

Run and debug it

same idea as 05AB1E, but Stax has more convenient output here :)

Explanation

Wi^p"+1/
W        loop forever
 i^      increment counter
   p     print without newline
    "+1/ print "+1/" without newline

answered Apr 30, 2021 at 7:41

Razetime

27.4k3 gold badges29 silver badges72 bronze badges

Add a comment |

chunes · Accepted Answer · 2021-04-30 23:16:46Z

1

Factor, 33 bytes

1 [ dup "%u+" printf 2 / t ] loop

Try it online!

1 Push 1 to the stack.
[ ... t ] loop The shortest infinite loop available in Factor.
dup "%u+" printf Non-destructively write the prettyprinted form of an object with a "+" afterward.
2 / Divide by two. In Factor, / produces an exact ratio as long as its inputs are rational. Use /i for integer division or /f to force the result to be a float.

answered Apr 30, 2021 at 23:16

chunes

26.8k3 gold badges24 silver badges53 bronze badges

Add a comment |

DLosc · Accepted Answer · 2021-05-01 00:36:55Z

1

Zephyr, 52 bytes

set i to 1
while 1=1
print i,"+"
set i to i/2
repeat

Try it online!

Gotta love built-in rational numbers.

For +3 bytes, output with all spaces (no newlines): Try it online!

answered May 1, 2021 at 0:36

DLosc

39.2k5 gold badges83 silver badges141 bronze badges

Add a comment |

ZaMoC · Accepted Answer · 2017-05-16 21:43:30Z

0

Mathematica, 45 bytes

Row@Flatten@Table[{1/2^t,"+"},{t,0,Infinity}]

edited May 16, 2017 at 21:43

answered May 16, 2017 at 12:12

ZaMoC

24.9k2 gold badges30 silver badges81 bronze badges

\$\begingroup\$ This will not finish computing, and nothing will be printed. \$\endgroup\$
– JungHwan Min
Commented May 16, 2017 at 13:53
\$\begingroup\$ Yes, I made it this way in order to get the result in a row. If you want to see a result just test for a finite number. Do you have any other ideas of how to print in a row? \$\endgroup\$
– ZaMoC
Commented May 16, 2017 at 14:03
1

\$\begingroup\$ You can use newlines as delimiters \$\endgroup\$
– JungHwan Min
Commented May 16, 2017 at 14:05

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

0

cQuents, 13 bytes

|+1/=1:2^($-1

Try it online!

Explanation

|+1/            Set sequence join to "+1/"
    =1          Set first item in sequence to 1
      :         Mode : (sequence)
       2^($-1   Each item in the sequence equals 2 to the power of the index (1-based) of the current item minus 1
             )  Implicit closing parenthesis

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jul 3, 2017 at 20:21

Stephen

14k3 gold badges52 silver badges117 bronze badges

Add a comment |

Stack Exchange Network

Infinitely Print Zeno's Dichotomy Paradox (1/(2^n))

Rules

51 Answers 51

Fourier, 20 bytes

Ruby 46 bytes

F#, 39 bytes

Labyrinth, 25 bytes

Common Lisp, 42 bytes

Explanation

PHP, 29 bytes

Ruby, 24 bytes

GNU Make, 45 57 bytes

MSX-BASIC, 36 bytes

Taxi, 916 bytes

Lua 5.1 + BC, 50 bytes

Cubix, 26 bytes

Clojure, 59 bytes

Husk, 9 bytes

MathGolf, 9 bytes

Perl 5 `-Mbigint`, 26 bytes

Stax, 7 bytes

Explanation

Factor, 33 bytes

Zephyr, 52 bytes

Mathematica, 45 bytes

cQuents, 13 bytes

Explanation

Your Answer

Not the answer you're looking for? Browse other questions tagged
code-golf
math
rational-numbers
or ask your own question.

Hot Network Questions

Infinitely Print Zeno's Dichotomy Paradox (1/(2^n))

Rules

51 Answers 51

Fourier, 20 bytes

Ruby 46 bytes

F#, 39 bytes

Labyrinth, 25 bytes

Common Lisp, 42 bytes

Explanation

PHP, 29 bytes

Ruby, 24 bytes

GNU Make, 45 57 bytes

MSX-BASIC, 36 bytes

Taxi, 916 bytes

Lua 5.1 + BC, 50 bytes

Cubix, 26 bytes

Clojure, 59 bytes

Husk, 9 bytes

MathGolf, 9 bytes

Perl 5 -Mbigint, 26 bytes

Stax, 7 bytes

Explanation

Factor, 33 bytes

Zephyr, 52 bytes

Mathematica, 45 bytes

cQuents, 13 bytes

Explanation

Your Answer

Sign up or log in

Post as a guest

Not the answer you're looking for? Browse other questions tagged code-golfmathrational-numbers or ask your own question.

Related

Hot Network Questions

Perl 5 `-Mbigint`, 26 bytes

Not the answer you're looking for? Browse other questions tagged
code-golf
math
rational-numbers
or ask your own question.