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

Wikipedia: Zeno's Dichotomy Paradox

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."

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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 , so shortest answer in bytes wins.

• Regarding the joke, I like the "You guys should know your limits" version better. May 16, 2017 at 13:17
• Is it just me, or is that a parabola right there?
May 16, 2017 at 14:17
• @StephenS Yes, I saw them too, but this one is much clearer and bigger.
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. 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 :) May 16, 2017 at 23:21

# 05AB1E, 10 9 bytes

Saved 1 byte thanks to Erik the Outgolfer

[No…+1/J?


Try it online!

Explanation

[           # loop over N infinitely [0 ...]
No         # calculate 2^N
…+1/J    # join with the string "+1/"
?   # print without newline

• You can golf this: [No?…+1/? May 16, 2017 at 12:04
• @EriktheOutgolfer: True! I knew that interpolation looked wasteful :P May 16, 2017 at 12:11
• Technically you should be using « instead of J but this works too. May 16, 2017 at 12:17
• @EriktheOutgolfer 'should use' isn't in a golfer's dictionary.
– Okx
May 16, 2017 at 15:59

# Python 2, 30 bytes

-5 thanks to Erik the Outgolfer

i=1
while 1:print i,'+1/';i*=2


Try it online!

# C (gcc), 60 bytes

f(){for(long long n=1;n;n*=2)printf(&"+1/%llu"[n^1?0:3],n);}


Goes up the the unsigned 64bit limit.

Try it online!

This one goes on forever; (it's as small as it's going to get)

# C (tcc), 312264255251233231208204195190188 170 bytes

l=4;c;main(i){for(char*t="*\b1+";puts(i=t),*++t=48;l=asprintf(&t,"1/%s",t+=*++t<49))for(t+=l-2;--t>i;)*t>52?*t=*t*2%58+c,c=*--t>52,*t=*t%48*2%10+49:(*t=*t*2-48+c+(c=0));}


Try it online!

Here's the not so golfed version;

c;l=4;main(i){
for(char*t="*\b1+";puts(i=t),*++t=48;l=asprintf(&t,"1/%s",t+=*++t<49))
for(t+=l-2;--t>i;)
*t>52?*t=*t*2%58+c,c=*--t>52,*t=*t%48*2%10+49:(*t=*t*2-48+c+(c=0));
}


# Jelly, 12 bytes

‘;“+1/”ȮḢḤ’ß


Try it online!

# Pyth, 10 bytes

.V0^2b"+1/


Try it online!

# APL (Dyalog Unicode), 15 bytes

More fun if ⎕FR (Floating-point Representation) is 1287 (128 bit decimal) and ⎕PP (Print Precision) is 34.

{∇2×⊃⎕←⍵'+1/'}1


Try it online!

{}1 apply the following function on the number 1:

⎕←⍵'+1/' print the argument and the the string

⊃ pick the first one (i.e. the argument)

2× double that

∇ tail call recursion on that (optimised, so it can be infinitely repeated)

# Bash, 33 bytes

echo 1;yes|awk '{print"+1/"2^NR}'


Try it online!

Change print for printf and echo for printf to avoid newline

• printf 1 also avoids the newline, no?
– Neil
May 16, 2017 at 14:59
• On my Awk (GNU Awk 4.2.1), I get repeated +1/inf from the 1024th term onwards. :-( Apr 3, 2019 at 15:58

# dc, 19 18 bytes

1[rdp+[+1/]Prdx]dx


## Explanation

We push 1 and [rdp+[+1/]Prdx] onto the stack. We then duplicate and execute [rdp+[+1/]Prdx]. The first thing it does is to rotate the stack (r) so that the value is on top. dp+ prints the value and adds itself (to multiply by 2). [+1/]P prints the invariant +1/, then we rotate the arguments so the saved macro definition is at the top, duplicate it and start again.

## Notes

GNU dc will normally wrap at 70 columns. To override that and get an infinite line, add DC_LINE_LENGTH=0 to your environment variables.

## Output (partial)

1
+1/2
+1/4
+1/8
+1/16
+1/32
+1/64
+1/128
+1/256
+1/512
+1/1024
+1/2048
+1/4096
+1/8192
+1/16384
+1/32768
+1/65536
+1/131072
+1/262144
+1/524288
+1/1048576
+1/2097152
+1/4194304
+1/8388608


...

+1/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512
+1/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024
+1/4171849679533027504677776769862406473833407270227837441302815640277772901915313574263597826048
+1/8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096
+1/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192
+1/33374797436264220037422214158899251790667258161822699530422525122222183215322508594108782608384


...

+1/39508742960703973701699058249321147362308454847936695835596789444561799223775119383138339311531617762178533629297475770286145628088251144169939127129573351351249626456638593338094796526172345495933122070775929580836041561599159299077777828204070582743494963385663317626578994458063693594803196645315374243921729198658112825073342949389812045193177027475122956756923784327372961582710038182537333922141259552951298907303962304838080273638036760780116072004845095527233255588553482279296774697359782192465695997942318865695221244129734666070151871832662077408140671163928915923237432567622143064546106133941951721500522645450228508984172259490047633694700073310127973759870498531879627921659506889467789827772217974527938921063212560947657822971770488425182948365680848383370895735146874307161886839006536947855165776686876541793136811167263580571304093957605985666196690184928497442785360764093478017451017746734495498153095432458734678594349803378385365288877714481483657768524929803674839527329386788921377623659662146451386624096645456088162412346874407275939999997795291704727515081702280114195915760730429971004053680396194153924851183822814089628520891784451651635432882834189518985962518491913745942769608364517349644317316883786394188027676315875802300614941521167533068776637714822997427956604900326486460019184026748377784334267448781151607331163551531249017855289595742337389988164318002911475316716184901518510216506967810214179264582001641604756838614530649510787748710515970103343413387907629523554359272907613750422053342161896933352596651762204311019492086408490451558722795552457312304151493327720013539795791396780129219445263809178656123790439902010266636225369198929939010768486889471574583687740703237723884060884341313109270396042776985369907837483449193699604446325434929715621310327967316917850518470187214490004577110243561029618419720922752928800741506704602272258298159626952200574962798177352636643822057543717726388960413069933543259522625754349233326342205092206727017922426027514405659437983511440608344700472705601338936605686966987172124738772188516007048230320749819398162536814976710592597538734137705950027359014588059062707620255218965805767357796513747447844523027915137840821345660865344374642005264231547974191720135374131636753072733967472098468431960701445604771410636863217872933622336548752977495855780251562187680752211721969296325463600172622609537613191880378481131363367650069328868188689922987810873631614557359705328210279446539258010268136177047368192438059279482528102638992531928429557597690537180509886930955777942766788025773602355396907906599024775244247870956027189054457531975304478521371381521485353149305097709658931812220918262294486689602972745683542729705723801006740031632845873373515192486849474031812571748034543997685658809569510355793325451872403514779086790086080249085626688289527240523390934950310034283577812811345070405593391658025105124251311424792323428537521834833098496849926115166627987693425225164221065888040679817710055149311700218473229573882735007326736184826228276198795800430996351794893869878616496964408658079755593435250740266925743063669693033962166638727208958848108618279706541681952402424403951452727855528325863478625420852111034874224126332581600270993719540233767913017317031917301947314301381305395778148662411240099861212350963538319161122105525140542957498243160511121081190999873793463700982194274391610079035649378156907404302109291456549051145972206937941256836207058890582488706269225196655757106314491362835961785278224285066734724349363542317085673599144544341787159375484193012654526110097825033479040113441770808525499628054646905495343469874033800453592330413492501029466619548807703349840857340023090845637275878427551483951820919716838598680072870886448655557475103895987586594457323290438277217416546924072119126008341434351372116758820210364483921779586954047645736749754706129527581706364540786199925444106851308928894123838719887248427406193523873241814252112960242471157146353688570100448110981388797252642426883393630199994048973788819157093688848496407354840126057329475558680721916931454066842963283515754585176372242775627387907273143150575761016992207751724577096752997060539405477817135276919229706042957713879187001161593522722567120109358147997326512389975917858806062700348362448471895255353617508014155741101819511284391838733058694543470468138671203784913218615013226104282579286537264875430408731136448578391399523220650329513170358814645003789376544233562516359743496023216403186793980621303443495530465939251724808374274310458025502798481081725847371166851046629335315923068250771335653634693337322262107406949362155173289000790264289820372935353554150505523064644792733552895751817412405124032479006980345444326870503243741298708595698623165439665394544936179141938567338846215386320683815738357770604967341613719725594913660580596082665203735813088294781572483642298773982857912441051544424056641771245170643793444471505411285243737462083781831896533323303672072505718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7029604801221984100983880306551144728065542617917554688


...

• i was 15 minutes late T_T, use dp instead of ddn to save a byte May 16, 2017 at 15:53
• I used dn to avoid introducing a newline, but did consider p (at the cost of uglier output). Actually, on reflection, it's not so ugly, after all. May 16, 2017 at 16:00

# JavaScript (ES6), 36 34 bytes

for(a=1;;a*=2)console.log(a+'+1/')


Try it online!

Inspired by Jake Taylor's answer.

Note that this is limited by language since a is a floating-point variable, not an integer.

-2 bytes thanks to @Stefnotch.

• You can save 2 bytes by leaving out the brackets after console.log. for(a=.5;;)console.log${a*=2}+1/ Though, your solution is limited by the language, because a is a float, not a big integer. (The challenge says that it should not be limited by the language, but rather by the system's specs.) May 17, 2017 at 15:58 • @Stefnotch That doesn't work unfortunately, because tagged templates with interpolation pass more than a single argument. I added the note about limitedness though, thank you. May 17, 2017 at 16:17 • Oh, sorry for not testing my code. Well, this code does shave off 2 bytes: for(a=1;;a*=2)console.log(a+"+1/") May 17, 2017 at 16:44 • @Stefnotch Oh, and it's a lot simpler, too :) Thank you. May 17, 2017 at 17:02 # GolfScript, 19 bytes 1{.'+1/'+puts.+.}do  Try it online! # CJam, 14 bytes 1{_o"+1/"o2*}h  Try it online! # ><>, 14 bytes 1:n"/1+"ooo2*!  Try it online! # Ruby, 27 25 bytes a=1;a*=2while$><<a<<'+1/'


Try it online!

# Pyth, 10 bytes

#h~hyZ"+1/


Z starts out as zero. ~hyZ post-assigns the value of 2*Z+1 to Z. Thus, Z becomes 0, 1, 3, 7, 15, ... over successive iterations. h then prints out the value one greater. # runs the infinite loop, and "+1/ gets the formatting right.

# Vim, 22, 21 bytes/keystrokes

qqyiwA+1/<esc>p@"<C-a>@qqxX@q


While testing this, you might run into issues with the current register values. To fix this, run

:let @q=''
:let @"=''


before running this, or by launching vim with

vim -u NONE -i NONE

• absolutely beautiful. May 18, 2017 at 17:08

# R, 35 34 bytes

cat(i<-1);repeat cat("+1/",i<-i*2)


Spacing is a bit werid but I understand that's ok.

• You can use repeat instead of while(T): cat(i<-1);repeat cat("+1/",i<-i*2) for 1 byte less. May 16, 2017 at 13:26

# AWK, 3732 bytes

BEGIN{for(;;)printf 2^i++"+1/"}


Try it online!

Could remove the BEGIN and save 5 bytes if input were allowed. Using exponents definitely cheaper byte-wise than multiplication. :)

Hopefully 2^1023 is close enough to infinity (on my work computer). Unfortunately the TIO link truncates earlier than that (around 921). But 17726622920963562283492833353875882150307419319860869157979152909707315649514250439943889552308992750523075148942386782770807567185698815677056677116184170553481231217950104164393978236130449019315710017470734562946173533283208371259654747728689409291887821024109648618981425152 does seem pretty close to infinity. :)

# Powershell, 34 bytes

for([bigint]$i=1;;$i*=2){"$i+1/"}  Try it online! # Go, 102 100 bytes Go can be almost as bad as Java, apparently. import(."fmt" ."math/big") func main(){n:=NewInt(1);for{Print(n.String()+"+1/");n.Mul(n,NewInt(2))}}  Try it online! (Would be a good idea to avoid running any of these locally. :P) • No, not as bad as Java: Go is 5 bytes shorter :P May 16, 2017 at 13:49 # Java, 107 102 bytes ()->{for(java.math.BigInteger z=null,o=z.ONE,n=o;;n=n.add(n))System.out.print(n.max(o)==o?1:"+1/"+n);}  z=null exists to shorten the o=java.math.BigInteger.ONE into z=null,o=z.ONE, saving 12 bytes. z.ONE will not throw a NullPointerException because we access a static member and not an instance one. Using int shortens the code, but fails to comply after 32 iterations. ## Saves • 107 -> 102 bytes: n.compareTo(o)>0 turned into n.max(o)==o, thanks to an idea given by @Shufflepants • This looks like one of the only entries that attempts to meet the rule: ""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." but it still doesn't do that because BigInteger still has a max value of 2^(Integer.MAX_VALUE). May 16, 2017 at 14:46 • @Shufflepants Where is that limit written? Nowhere ("may support values outside of that range"), so it's not a limitation of the language, but a limitation of the JVM, which then is the system. Also, "works on my computer", so good enough for codegolf ;) May 16, 2017 at 14:55 • If the implementation of a language or the JVM is considered part of the system and not the language, then you might as well use int instead of BigInteger. May 16, 2017 at 15:00 • No, because int and all other primitive types are limited at the language level. Also, the BigInteger doc explicitly says that a limit is optional, not mandatory (and that the default JVM implementation uses that limit). May 16, 2017 at 15:04 • This function "BigInteger max(BigInteger val)" exists in the specification too, which implies, that while the limit need not be what the current implementation limit is, it implies in the specification that there must be some finite limit. May 16, 2017 at 15:07 # C#, ̶6̶8̶ 154 bytes void A(int b=1){System.Console.Write($"1{(b>1?"/"+b:"")}+");A(b*2);}


Here is a version not constrained by int

using System.Numerics;BigInteger b=new BigInteger(1);void A(){System.Console.Write($"1{(b>1?"/"+b:"")}+");b=BigInteger.Multiply(new BigInteger(2),b);A();}  • Stops working very quickly once the denominator hits int.MaxValue – Rob May 17, 2017 at 4:55 • @Rob what should the behavior be? May 17, 2017 at 4:58 • Here's an example: codegolf.stackexchange.com/questions/120796/… – Rob May 17, 2017 at 4:58 • Okay thanx, the new version should be sufficient. May 17, 2017 at 7:10 • As-is, nothing is actually printed because there's no call to A(); outside of the recursive call in the function. Also, BigIntegers have implicit conversions from primitive numeric types and built-in operators. So you can shave a lot (54 bytes?) off by changing the initial declaration to just BigInteger b=1; and shortening the multiplication to b*=2; May 17, 2017 at 15:16 # JavaScript (ES6), 4543 42 bytes Saved 2 bytes, thanks @DanielM ! Saved 1 byte, thanks @eush77 for pointing it out. =console.log;a=1;(1);for(;;)_(+1/${a*=2})

=console.log;(a=1);for(;;)_(+1/${a*=2}) _=console.log;for(_(a=1);;)_(+1/${a*=2})


My first go at Codegolf, go easy!

• I was going to edit a snippet in for you, but then I broke my browser and remembered this is an infinite loop question xD May 16, 2017 at 13:37
• Yeah, had to restart my dev tools a couple times doing this! May 16, 2017 at 13:42
• The a=1 can go in the first part of the for, for(a=1;;) saving you a byte in extra semicolon. May 16, 2017 at 14:55
• _(a=1), work's with DanielM's suggestion too May 16, 2017 at 16:00
• @eush77 That doesn't create the right output imo. It will always have a trailing +1/, not a fraction. May 17, 2017 at 8:17

# PHP, 32 Bytes

for(;;)echo bcpow(2,$i++)."+1/";  Online Version -6 Bytes if values like 9.2233720368548E+18 are allowed for(;;)echo 2**$i++."+1/";


Try it online!

# Befunge 93: 14 bytes

1:.2*"/1+",,,#

• Doesn't seem to be working on TIO. Is it written for some specific implementation? May 19, 2017 at 16:39
• @eush77 Looks like TIO expects a fixed 80 char width grid, causing the "#" to skip empty space instead of the next instruction. I usually test here, where the torus is adjusted to the size of the actual code. May 22, 2017 at 10:00

# Jelly, 11 bytes

o©1“+1/”Ḥɼß


Try it online!

## How it works

Jelly's parsing rules are very complicated and depend on the arities of the link. Usually, links are composed of collections of:

• Dyad-nilad pairs (arities 2, 0) such as ÷4 (divide by 4)
• Nilad-dyad pairs (arities 0, 2) such as 3< (greater than 3)
• Monads (arity 1) such as L (length)
• Dyad-monad and monad-dyads (arities 2, 1 and 1, 2) such as +H or H+ (both $$\n + \frac n2\$$)

However, sometimes (very rarely), the arity patterns don't make sense. This is referred to an "unparseable" link. One such example is

4 H 5 Ḥ


Try it online!

The arities here are 0, 1, 0, 1, and the second nilad doesn't fit into any of the patterns. In this case, 5 is called an "unparseable nilad", and it causes the program to output the previous value (4H, or 2) and discard it, using the 5 as the new link value. This causes the program about to output 210 (4H outputs 2 and 5Ḥ outputs 10 at the end of the program)

The arities of the program above are 2, 0, 0, 0, 1. The pattern 0, 0, 0 is unparseable, meaning that the third and fourth links (“+1/” and Ḥɼ) are unparseable nilads

o©1“+1/”Ḥɼß - Main link f(n). Initially n = 0
o 1         - Replace 0 with 1
©          - Save this value into the register
“+1/”    - Unparseable nilad; Output 1 and use "+1/" as the argument
Ḥɼ  - Unparseable nilad; Output "+1/" and use the below result as the argument:
ɼ  -   Run the previous command on the register, then save the result back into the register:
Ḥ   -     Unhalve; Yield 2n
ß - Recurse, yielding f(2n)


# Aceto, 20 bytes

 pL*
pd12<
p"M"
1+1/


Prints the sequence without any spaces. When run, you won't see anything for a little while, because of buffering, run with -F to immediately see everything.

1. Pushes and prints a 1, then stores "+1/" in quick storage (the register).
2. Pushes a 1.
3. Multiplies by two, loads from the register, prints, duplicates, and prints.
4. GOTO 3.

## QBIC, 18 bytes

?1{q=q*2?@+1/';q


Prints each term on a new line.

Explanation:

?1       Prints 1
{        Infinite loop
q=q*2    Doubles q, starts at 1*2=2
?@+1/  Prints the string +1/
';      without tabs, newlines or other terminators (code literal, ; is a QBIC function)
q        Also prints q
The infinite loop is auto-closed by QBIC at EOF.


We can save a byte with a more liberal output format:

{?q,A,┘q=q*2#+1/


# Mathematica, 25 bytes

1//.n_:>(n~Print~"+";n/2)

• Don't we have to print the +s as well as the numbers? May 16, 2017 at 17:04
• @GregMartin Fixed... May 16, 2017 at 18:39

## Haskell - 66626051 49 chars

import Data.List
main=print$intercalate" + 1/"$map(show.(2^))[0..]


This prints the string constructed by printing the string representations of the powers of two starting from 1, separated by the string " + 1/".

The code itself is 49 bytes, the import and newline push it up to 66

## Edit: (62)

Shaved 4 bytes by cutting out the import and defining intercalate with a much shorter name

f(x:xs)s=x++s++xsfs
main=print$map(show.(2^))[0..]f" + 1/"  ## Edit 2: (60) Shaved 2 more characters by realizing I didn't need to use the (x:xs) list convention: f(x:y)s=x++s++yfs main=print$map(show.(2^))[0..]f" + 1/"


## Edit 3: (51)

Reimplemented the definition of f and the map as the body of a fold to save 9 more characters

main=print$foldr((++).(++" + 1/").show.(2^))""[0..]  ## Edit 4: (49) As was pointed out by Laokoni, I can remove the spaces to cut down 2 more bytes off the total: main=print$foldr((++).(++"+1/").show.(2^))""[0..]

• The challenge states that spaces in the output are optional, so you can save another two bytes. May 18, 2017 at 7:04
• Also noticed that the most recent version is the same number of bytes as the original would be if "intercalate" was in the Haskell base library. May 18, 2017 at 19:34

# Braingolf, 41 37 bytes

Saved 4 bytes because I realised I don't need the spaces, always read the spec thoroughly kids

1!_V"+/">!@R.[<!_>2*v<!@>R!_v!@R<1+>]


Try it online!

Can probably be golfed better, but it works.