• Post Reply Bookmark Topic Watch Topic
  • New Topic

Does 1.0 equal 0.9999999999999999...?  RSS feed

 
Robert James Liguori
Author
Ranch Hand
Posts: 587
6
Java Netbeans IDE Oracle
 
Campbell Ritchie
Marshal
Posts: 56529
172
  • Likes 2
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
No, they are not equal. What you are seeing is the inability of the floating‑point datatypes to distinguish such small differences.
 
Campbell Ritchie
Marshal
Posts: 56529
172
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Surely you shou‍ld have written
if (bigDecimal1.compareTo(bigDecimal2) != 0) ...
rather than using <. It still shows not equal.
 
Jesper de Jong
Java Cowboy
Sheriff
Posts: 16058
88
Android IntelliJ IDE Java Scala Spring
  • Likes 1
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Campbell Ritchie wrote:No, they are not equal.

Actually, 0.9999...... (infinitely repeating 9's) is equal to 1.

But the program in the blog is not really showing that, because it isn't working with the number 0.9999...... (infinitely repeating 9's), but with an approximation with a finite number of 9's.

 
Jeanne Boyarsky
author & internet detective
Marshal
Posts: 37462
537
Eclipse IDE Java VI Editor
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Fun! That's a lot of 9's in your blog post!
 
fred rosenberger
lowercase baba
Bartender
Posts: 12563
49
Chrome Java Linux
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
regardless of how many 9's there are in that post, that's not even CLOSE to an infinite number of 9's.

I haven't watched the video, but there are a couple of simple ways to show that 0.999... is exactly 1. The simplest relise on the fact that multiplication and division are inverse operations.  If I divide by 2, then multiply by 2, i get back my original number. That is a fundamental property of multiplcation.

so, i can take a number...Say 1, and divide it by 3, then multiply that result by three, and i'm back to my original number.

1 / 3 = 0.33333....and on and on forever.

0.3333...and on and on forever * 3 is 0.9999....and on and on forever. And so it must equal 1.
 
Campbell Ritchie
Marshal
Posts: 56529
172
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Jesper de Jong wrote:. . . (infinitely repeating 9's) is equal to 1. . . . an approximation with a finite number of 9's. . . .
Yes, that is the problem. It sh‍ould be possible to show that all finite sequences of multiple 9s after the decimal point do not equal 1.0.
  • 1: 0.999999999999999999 = 1.0 (Assumption)
  • 2: 0.9999999999999999999 is closer to 1.0 ∴ 0.9999999999999999999 = 1.0
  • 3: 0.999999999999999999 ≠ 0.9999999999999999999  (Arithmetic)
  • 4: 1.0 = 1.0 (Arithmetic)
  • 5: 1.0 ≠ 1.0 (Deduction from lines 1, 2, and 3)
  • 6: 0.999999999999999999 ≠ 1.0 (Reductio ad absurdum of assumption 1 under 4 and 5)
  •  
    fred rosenberger
    lowercase baba
    Bartender
    Posts: 12563
    49
    Chrome Java Linux
    • Likes 1
    • Mark post as helpful
    • send pies
    • Quote
    • Report post to moderator
    Campbell Ritchie wrote:Yes, that is the problem. It sh‍ould be possible to show that all finite sequences of multiple 9s after the decimal point do not equal 1.0

    it should be simpler than that.

    1 - 0.<x nines> = 0.<(x-1) zeros>1

    I think i have that right...

    so if there is a non-zero difference between two number, they are not the same.
     
    Campbell Ritchie
    Marshal
    Posts: 56529
    172
    • Mark post as helpful
    • send pies
    • Quote
    • Report post to moderator
    Yes, that looks right. If x is ∞ however, 0.0...01 degenerates to 0.0 and the two numbers become mutually equal.
     
    Randall Twede
    Ranch Hand
    Posts: 4696
    8
    Java Scala
    • Mark post as helpful
    • send pies
    • Quote
    • Report post to moderator
    i was just gonna mention that infinity problem. i dont want to take sides in this argument
     
    Stephan van Hulst
    Saloon Keeper
    Posts: 7969
    143
    • Mark post as helpful
    • send pies
    • Quote
    • Report post to moderator
    There is no argument here Randall :)

    There is a mathematical proof that 0.‾9 is equal to 1, so there is no side to pick. It's just a fact.
     
    Henry Wong
    author
    Sheriff
    Posts: 23295
    125
    C++ Chrome Eclipse IDE Firefox Browser Java jQuery Linux VI Editor Windows
    • Mark post as helpful
    • send pies
    • Quote
    • Report post to moderator
    Stephan van Hulst wrote:
    There is a mathematical proof that 0.‾9 is equal to 1, so there is no side to pick. It's just a fact.


    Yeah, there are lots of proofs out there -- including one using 9th grade algebra. So, most 14 and 15 year old children (in the U.S. that is, other countries may be younger) knows this fact...

    Henry
     
    • Post Reply Bookmark Topic Watch Topic
    • New Topic
    Boost this thread!