Zeno의 이분법 역설을 무한대로 인쇄 (1 / (2 ^ n))

31

위키 백과 : Zeno의 이분법 역설

수많은 수학자들이 술집에 들어갑니다. 첫 번째는 맥주를 주문합니다. 두 번째는 반 맥주를 주문합니다. 세 번째는 맥주의 1/4을 주문합니다. 바텐더는 그들을 막고 맥주 두 잔을 부으며 "당신은 모두 바보입니다."

레딧

프로그램이 실행되는 동안 각 항목의 분모에 매번 2를 곱하여 다음 시리즈를 인쇄하십시오.

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

같이 n무한대에 접근이 시퀀스의 합은 접근 2.

규칙

아니요, 인쇄 할 수 없습니다 2.

1/1첫 번째 항목으로 인쇄하지 못할 수 있습니다 .

필요에 따라 1+1/2+...공백 1 + 1 / 2 + ...을 제거 하거나 공백 을 추가 할 수 있습니다.

대중적인 수요로 인해 공백 대신 줄 바꾸기를 구분 기호로 사용할 수 있습니다.

당신은 추가 할 수 .의 플러스 상수 0필요가있을 경우 분모에들.

"무한"이란 불필요한 지연이없고, 현재 (가변) 시스템 사양에 의해 가능한 한 오랫동안 제한되지만 현재 언어에 의해 제한되지는 않습니다.

표준 허점이 적용됩니다.

이것은 code-golf 이므로 바이트 단위의 최단 답변이 이깁니다.

code-golf  math  rational-numbers 
— 스티븐
소스
41
농담에 관해서는, 나는 "당신은 당신의 한계를 알아야한다"버전을 더 좋아합니다.
— March Ho
14
그것은 단지 나, 아니면 그 포물선 권리 가 ?
— Adám
1
@StephenS 예, 저도 보았지만 훨씬 명확하고 커졌습니다.
— Adám
10
@ Adám : p! 분모의 길이가 변하지 않았다면, +1/s 의 시각적 패턴 은 단지 대각선을 형성 할 것입니다. 그러나 분모의 길이는 선형으로 (반올림까지) 변 합니다. 자릿수 2^n는 약 n log(2)/log(10)입니다. 그 변화는 선형으로 변환 선형 변화에 대하여 각각의 위치 +1/A와 동일 항 하나에 대하여 이차 변화 절대 위치.
— Greg Martin
3
@QPaysTaxes 당신은 경쟁이 아닙니다-그러나 여러 사람들이 경쟁 C 답변을 게시하려면 서로 경쟁 할 수 있습니다 :)
— Stephen

답변:

14

05AB1E , 10 9 바이트

Outgolfer Erik 덕분에 1 바이트 절약

[No…+1/J?

온라인으로 사용해보십시오!

설명

[           # loop over N infinitely [0 ...]
 No         # calculate 2^N
   …+1/J    # join with the string "+1/"
        ?   # print without newline
— 에미 냐
소스
당신은 이것을 골프 수 있습니다 :[No?…+1/?
— Outgolfer Erik
@EriktheOutgolfer : 맞아요! 보간이 낭비되는 것처럼 보였습니다. : P
— Emigna
1
기술적으로 당신은 «대신 사용해야 J하지만 이것은 작동합니다.
— Outgolfer Erik
13
@EriktheOutgolfer 'should use'은 (는) 골퍼의 사전에 없습니다.
— Okx
6

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)

— Adám
소스
6

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), 312 264 255 251 233 231 208 204 195 190 188 170 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));
}
— cleblanc
소스
5

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

— marcosm
소스
1
printf 1 also avoids the newline, no?
— Neil
On my Awk (GNU Awk 4.2.1), I get repeated +1/inf from the 1024th term onwards. :-(
— Toby Speight
5

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

...

— Toby Speight
소스
i was 15 minutes late T_T, use dp instead of ddn to save a byte
— Felipe Nardi Batista
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.
— Toby Speight
4

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.

— isaacg
소스
4

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.

— eush77
소스
1
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.)
— Stefnotch
1
@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.
— eush77
1
Oh, sorry for not testing my code. Well, this code does shave off 2 bytes: for(a=1;;a*=2)console.log(a+"+1/")
— Stefnotch
@Stefnotch Oh, and it's a lot simpler, too :) Thank you.
— eush77
3

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
— Olivier Grégoire
소스
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).
— Shufflepants
@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 ;)
— Olivier Grégoire
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.
— Shufflepants
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).
— Olivier Grégoire
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.
— Shufflepants
3

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
— DJMcMayhem
소스
1
absolutely beautiful.
— Tyrannosaur
3

R, 35 34 bytes

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

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

— Masclins
소스
1
You can use repeat instead of while(T): cat(i<-1);repeat cat("+1/",i<-i*2) for 1 byte less.
— plannapus
3

Befunge 93: 14 bytes

1:.2*"/1+",,,#
— karhell
소스
Doesn't seem to be working on TIO. Is it written for some specific implementation?
— eush77
@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.
— karhell
2

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.
— L3viathan
소스
2

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)

— totallyhuman
소스
No, not as bad as Java: Go is 5 bytes shorter :P
— Olivier Grégoire
2

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/
— steenbergh
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2

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();}
— LiefdeWen
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Stops working very quickly once the denominator hits int.MaxValue
— Rob
@Rob what should the behavior be?
— LiefdeWen
— Rob
Okay thanx, the new version should be sufficient.
— LiefdeWen
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;
— goric
2

JavaScript (ES6), 45 43 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!

— Jake Taylor
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3
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
— Stephen
2
Yeah, had to restart my dev tools a couple times doing this!
— Jake Taylor
The a=1 can go in the first part of the for, for(a=1;;) saving you a byte in extra semicolon.
— DanielM
_(a=1), work's with DanielM's suggestion too
— Felipe Nardi Batista
@eush77 That doesn't create the right output imo. It will always have a trailing +1/, not a fraction.
— Jake Taylor
2

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. :)

— Robert Benson
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2

Haskell - 66 62 60 51 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++xs`f`s
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++y`f`s
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..]
— archaephyrryx
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The challenge states that spaces in the output are optional, so you can save another two bytes.
— Laikoni
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.
— archaephyrryx
1

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.

— Skidsdev
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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
— Beta Decay
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Can you not move the Print i to the start of the While loop?
— Neil
@Neil I could, but it wouldn't say any bytes
— Beta Decay
Oh, I see now, you're not actually printing i.
— Neil
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