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| Is 0.999... = 1 ? |
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Frant
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 Posted: Sun, 10th Apr 2011 23:40 Post subject: 0.999... = 1 or not? |
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This is one of those issues that defies intuitive logic. What's your take on it?
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!
"The sky was the color of a TV tuned to a dead station" - Neuromancer
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garus
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| Posted: Sun, 10th Apr 2011 23:49 Post subject: |
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snip
Last edited by garus on Tue, 27th Aug 2024 21:49; edited 1 time in total
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| Posted: Sun, 10th Apr 2011 23:56 Post subject: |
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In mathematics it's maybe one, but to say that in physics would be a suicide...
You'd be making your measurements less precise on purpose.
Then again measurements without error have no meaning. For instance you cannot say that 0.99895+-0.002352 = 1.000+-0.002 - you'd flunk the statistics and every lab exercise here. It's 0.999+-0.002...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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| Posted: Mon, 11th Apr 2011 00:10 Post subject: |
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You don't lose precision. It's just how it is by definition.
9 * 1/9 = 1
since
1/9 = 0.111...
you can write the first equation as
9 * 0.111... = 0.999...
and since first and third equation are equivalent
9 * 1/9 ~ 9 * 0.111...
it stands
1 = 0.999...
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Frant
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| Posted: Mon, 11th Apr 2011 00:52 Post subject: |
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Because it isn't a single number, it all depends on what you're doing to compare/calculate 0.999... and 1.
0.999... < 1
1 > 0.999...
0.999... * 1 = < 1
1 - 0.999... = 0.000...1
and so on.
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!
"The sky was the color of a TV tuned to a dead station" - Neuromancer
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| Posted: Mon, 11th Apr 2011 01:29 Post subject: |
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| Frant wrote: | Because it isn't a single number, it all depends on what you're doing to compare/calculate 0.999... and 1.
0.999... < 1
1 > 0.999...
0.999... * 1 = < 1
1 - 0.999... = 0.000...1
and so on. |
The problem is, 0.000...1 would have to mean "infinitesimal difference". Which is something that doesn't exist in a real number system (assuming we're not talking about some obscure number system). Only possible "difference" between the two numbers is zero.
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Frant
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| Posted: Mon, 11th Apr 2011 01:35 Post subject: |
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In physics and probability 0.999... doesn't automatically equal 1. It seems like it's simply an easy solution to make sense of numbers and problems that borders on paradoxical. In a normal Real number system 0.999... might as well be 1 (and is) since 0.999... is nonsensical in that context.
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!
"The sky was the color of a TV tuned to a dead station" - Neuromancer
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| Posted: Mon, 11th Apr 2011 07:43 Post subject: |
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In physics it's not all that often that you come about 0. infinetly many 9's. It doesn't make sense as a measurement and when deriving formulars you use ordinary math, so of cause 0.999... = 1 in physics to.
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aevis
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Location: Absurdia
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| Posted: Mon, 11th Apr 2011 10:32 Post subject: |
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| Atropa wrote: | | In physics it's not all that often that you come about 0. infinetly many 9's. It doesn't make sense as a measurement and when deriving formulars you use ordinary math, so of cause 0.999... = 1 in physics to. |
Again if you're doing measurement you need error and then you can round things all you want 
E.g.
25.3587*0.99999=25.3584 so there is a discrepancy, but only because of the finites of the number.
In physics ppl like to round things even worse. My professor once did an approximation that used 2*pi=10  But in the end if you get good order of magnitude you're fine and you can say: nobody's perfect
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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| Posted: Mon, 11th Apr 2011 11:42 Post subject: |
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| Posted: Mon, 11th Apr 2011 11:47 Post subject: |
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| Atropa wrote: | | dingo_d wrote: |
In physics ppl like to round things even worse. My professor once did an approximation that used 2*pi=10 But in the end if you get good order of magnitude you're fine and you can say: nobody's perfect |
2*pi=10 seems weird however pi^2=10 is fine by me. I haven't calculated anything but order of magnitude for years  . Can't be bothered with numerics. |
That's called crude approximation
Oh and we do everything numerically here  I hate numerics, but hey all the interesting stuff isn't analytically solvable...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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| Posted: Mon, 11th Apr 2011 12:24 Post subject: |
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This is a troll equation, both awnsers are valid depending in what context they are used. It all depends on wether you accept infinitesimal differences or not. Posting this without context is like posting the word Cock and then giving the options : a Penis or a Rooster.
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LeoNatan
☢ NFOHump Despot ☢
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| Posted: Mon, 11th Apr 2011 14:48 Post subject: |
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Rofl_Mao
Posts: 3187
Location: Nederland
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| Posted: Mon, 11th Apr 2011 14:55 Post subject: |
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| BearishSun wrote: | | Frant wrote: | Because it isn't a single number, it all depends on what you're doing to compare/calculate 0.999... and 1.
0.999... < 1
1 > 0.999...
0.999... * 1 = < 1
1 - 0.999... = 0.000...1
and so on. |
The problem is, 0.000...1 would have to mean "infinitesimal difference". Which is something that doesn't exist in a real number system (assuming we're not talking about some obscure number system). Only possible "difference" between the two numbers is zero. |
 <aha-erlebnis
Ha, I get it now. Infinitesimal difference... What a beautiful concept. A quantity so small, it doesn't exist in the real world
| Lopin18 wrote: | I think you played too much Fallout 3, Pedo Perk acquired.  |
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deelix
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| Posted: Mon, 11th Apr 2011 15:00 Post subject: |
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LeoNatan
☢ NFOHump Despot ☢
Posts: 73196
Location: Ramat Gan, Israel 🇮🇱
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| Posted: Mon, 11th Apr 2011 15:13 Post subject: |
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| deelix wrote: | | iNatan wrote: | | The fuck is this "" !? |
woot, is this a mods work |
nop. |
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| Posted: Mon, 11th Apr 2011 15:18 Post subject: |
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| iNatan wrote: | | deelix wrote: | | iNatan wrote: | | The fuck is this "" !? |
woot, is this a mods work |
nop. |
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| Posted: Mon, 11th Apr 2011 15:21 Post subject: |
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| BearishSun wrote: | | Frant wrote: | Because it isn't a single number, it all depends on what you're doing to compare/calculate 0.999... and 1.
0.999... < 1
1 > 0.999...
0.999... * 1 = < 1
1 - 0.999... = 0.000...1
and so on. |
The problem is, 0.000...1 would have to mean "infinitesimal difference". Which is something that doesn't exist in a real number system (assuming we're not talking about some obscure number system). Only possible "difference" between the two numbers is zero. |
Wouldn't be the difference between 0 and 0.000...1 = 0.000...1
because 0.000...1 - 0.000...1 = 0 |
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| Posted: Mon, 11th Apr 2011 15:46 Post subject: |
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| PumpAction wrote: | | BearishSun wrote: | | Frant wrote: | Because it isn't a single number, it all depends on what you're doing to compare/calculate 0.999... and 1.
0.999... < 1
1 > 0.999...
0.999... * 1 = < 1
1 - 0.999... = 0.000...1
and so on. |
The problem is, 0.000...1 would have to mean "infinitesimal difference". Which is something that doesn't exist in a real number system (assuming we're not talking about some obscure number system). Only possible "difference" between the two numbers is zero. |
Wouldn't be the difference between 0 and 0.000...1 = 0.000...1
because 0.000...1 - 0.000...1 = 0 |
It would. But 0.000...1 is not something that exists. Even the notation we're using here is made up. You can write it as dx in differential equations but you can't write infinitesimal difference in the form of an actual number.
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Frant
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| Posted: Mon, 11th Apr 2011 23:17 Post subject: |
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| aevis wrote: | | i believe it's the reason behind calculators returning 0.666667 when trying to do 2/3, for example. |
it's called rounding
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| Posted: Tue, 12th Apr 2011 03:16 Post subject: |
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You can say the limit approaches 1. But its technically incorrect to say that 0.9999999999 = 1. If you were to graph it and keep zooming in, the line would never actually touch 1.0
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SycoShaman
VIP Master Jedi
Posts: 24468
Location: Toronto, Canada
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| Posted: Tue, 12th Apr 2011 06:18 Post subject: |
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its not the same to me...999999 is exactly that. 1 is another integer value....its like saying is 1.99999 the same as 2.0....its not.
If u round the numbers then i suppose, but technically and imo/mind, i consider them separate values
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Neon
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Frant
King's Bounty
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