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EliasAndri
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 Posted: Thu Jun 18, 2009 6:55 am Post subject: |
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0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...
= 9·0.1 + 9·0.01 + 9·0.001 + 9·0.0001 + ...
= 9·10-1 + 9·10-2 + 9·10-3 + 9·10-4 + ...
n=∞
= Σ 9·10-n
n=1
n=N
:= lim Σ 9·10-n
N→∞ n=1
= lim ( 9·10-1 + 9·10-2 + ... + 9·10-N )
N→∞
= lim ( 9·0.1 + 9·0.01 + ... + 9·0.000...0001 )
N→∞ \________/
N digits
= lim ( 0.9 + 0.09 + ... + 0.000...0009 )
N→∞ \________/
N digits
= lim ( 0.999...999 )
N→∞ \_______/
N nines
= lim ( 1 - 0.000...0001 )
N→∞ \________/
N digits
= lim ( 1 - 10-N )
N→∞
= lim 1 - lim 10-N
N→∞ N→∞
= 1 - 0
= 1
SOURCE: http://qntm.org/index.php?pointnine
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oib111
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| Posted: Thu Jun 18, 2009 7:05 pm Post subject: |
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That seems overly complicated 
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Monkeys
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yuki953
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| Posted: Fri Jun 19, 2009 4:41 am Post subject: |
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| [SPW]Killamoocow wrote: | I forgot where I got this from but 0.999...("..." being repeated) = 1
1/3 in decimal form is obviously 0.333...
if you take
1/3 + 1/3 + 1/3 you get 1.
if you take 0.333... + 0.333... + 0.333... you get 0.999...
just proves how inacurate decimals can be  |
thats not a fair judgment because one of thoughs 1/3d would be 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334
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EliasAndri
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| Posted: Fri Jun 19, 2009 6:09 am Post subject: |
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| yuki953 wrote: | | [SPW]Killamoocow wrote: | I forgot where I got this from but 0.999...("..." being repeated) = 1
1/3 in decimal form is obviously 0.333...
if you take
1/3 + 1/3 + 1/3 you get 1.
if you take 0.333... + 0.333... + 0.333... you get 0.999...
just proves how inacurate decimals can be |
thats not a fair judgment because one of thoughs 1/3d would be 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334 |
No, because the answer is 0,33333...
... being infinity, and infinity never ends (unless you're Chuck Norris) so there is no 4, always just 3.
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yuki953
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| Posted: Fri Jun 19, 2009 6:43 am Post subject: |
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scientificaly it is .3333333-
but mathmaticaly corect... its .33333333-4
trust me.... you do not want to get into a science fight with me
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EliasAndri
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| Posted: Fri Jun 19, 2009 6:58 am Post subject: |
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1/3 is 0,3333333... (... being infinity)
You can't just make it stop being infinity and put a 4 there, it will always until the end of time be 3!
Mathematically it is 0,33333...
But 3/3 is 1!
Then 0,9999... must be 1.
Please read http://qntm.org/index.php?pointnine
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DanielG
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| Posted: Fri Jun 19, 2009 7:03 am Post subject: |
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| yuki953 wrote: | scientificaly it is .3333333-
but mathmaticaly corect... its .33333333-4
trust me.... you do not want to get into a science fight with me |
 what are you on about?
or are you trolling?
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SFP+
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| Posted: Fri Jun 19, 2009 9:49 am Post subject: |
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The whole 0.999999... being 1 discussion is ridiculous. 0.999999... is 0.999999... and 1 is 1.
Further shit:
You can look at this from different angles, mathematical seen, scientifically seen, logically seen, you can make as many theories as you want. 0.999.... does not equal to 1 One proof (1/3 = 0.33, 3/3 = 0.99) means nothing as decimals & fractions are two different counting methods. It's like comparing bones in fish & bones in chicken.
Last edited by SFP+ on Fri Jun 19, 2009 11:25 am; edited 1 time in total |
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AverageAzn247
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| Posted: Fri Jun 19, 2009 10:23 am Post subject: |
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| Safko wrote: | The whole 0.999999... being 1 discussion is ridiculous. 0.999999... is 0.999999... and 1 is 1.
Further shit:
You can look at this from different angles, mathematical seen, scientifically seen, logically seen, you can make as many theories as you want. 0.999.... does not equal to 1 One proof (1/3 = 0.33, 3/3 = 0.99) means nothing as decimals & fractions are two different counting methods. It's like comparing bones in fish & bones in chicken. |
When u convert from decimals to fractions a small rounding error occurs.
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Monkeys
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| Posted: Fri Jun 19, 2009 11:04 am Post subject: |
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There is no rounding error.
It just doesn't exist in the same system ;p
Basicly you're comparing an Unreal strict number to a Real number, which is not allowed, because of inaccuracies like this.
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EliasAndri
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| Posted: Fri Jun 19, 2009 11:11 am Post subject: |
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| Safko wrote: | The whole 0.999999... being 1 discussion is ridiculous. 0.999999... is 0.999999... and 1 is 1.
Further shit:
You can look at this from different angles, mathematical seen, scientifically seen, logically seen, you can make as many theories as you want. 0.999.... does not equal to 1 One proof (1/3 = 0.33, 3/3 = 0.99) means nothing as decimals & fractions are two different counting methods. It's like comparing bones in fish & bones in chicken. |
You sir, fail.
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oib111
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| Posted: Fri Jun 19, 2009 11:59 am Post subject: |
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Honestly did anybody read http://qntm.org/index.php?pointnine? Please read that before you come commenting on how .999999..... is not equal to 1, because you are obviously wrong.
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| 8D wrote: |
cigs dont make people high, which weed does, which causes them to do bad stuff. like killing |
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Monkeys
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| Posted: Fri Jun 19, 2009 12:08 pm Post subject: |
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| oib111 wrote: | | Honestly did anybody read http://qntm.org/index.php?pointnine? Please read that before you come commenting on how .999999..... is not equal to 1, because you are obviously wrong. |
And that site is hosted/content developed by?
That's probably just some dude collecting information everywhere.
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SFP+
Comp. talk moderator
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| Posted: Fri Jun 19, 2009 1:02 pm Post subject: |
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| oib111 wrote: | | Honestly did anybody read http://qntm.org/index.php?pointnine? Please read that before you come commenting on how .999999..... is not equal to 1, because you are obviously wrong. |
I read it, it's bullshit, 1 equals to 1. 0.9999* does not.
False -> 1.0000... - 0.9999... = 0.0000...
True -> 1.0000... - 0.9999... = 0,0001...
| Random wrote: |
No, it shouldn't. "0.0000...1" is meaningless. The "..." means the zeros go on forever. "Forever" means "without end". There IS no end for the final 1 to go on. |
If the zeros goes on forever, maths obviously can't solve the number as you don't even know what you're subtracting & what not.
| Random wrote: |
So, if 0.9999... and 1.0000... were different numbers, then it would be possible to find a number which was between them.
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What? That's like saying 0.353 & 0.354 are the same numbers as there is no number between them. Along with the fact that there is a number between them (an extra nine you fucking idiot)
| Sam Hguhes wrote: |
But it's impossible to write out the decimal expansion of a number between 0.9999... and 1.0000... .
Therefore, they cannot be different numbers.
Therefore, they are the same number. |
Oh hay! Here's nine goats, prove to me how those goats are really 10 goats. (That's what you're saying? You're skipping one of them?)
99+1 = 100, 9+1 = 10, 0.9 + 0.1 = 1 (Assuming there are as many decimals in the first number as it is in the second one.).
| Random wrote: |
"But on line two, 9.9999... should be 9.9999...0, because you multiplied it by ten!"
"9.9999...0" is meaningless. The "..." means the nines go on forever. "Forever" means "without end". There IS no end for the final 0 to go on. See the Preliminary note. |
For him, everything seems to be meaningless.
| Random wrote: |
1/3 = 0.3333...
1 = 3/3
= 3 * 1/3
= 3 * 0.3333...
= 0.9999...
Proof that 1/3 = 0.3333... is left to the reader.
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As I've already stated in a post above. You can't compare fractions & decimals.
As well as this ->
| Code: |
1/3 = 0.3333 | 2/3 = 0.6666 | 3/3 = 0.9999
which can also equal to
1/3 = 0.333 | 2/3 = 0.666 | 3/3 = 0.66
....
1/3 = 0.33 | 2/3 = 0.66 | 3/3 = 0.6
bla
1/3 = 0.3 | 2/3 = 0.6 | 3/3 = 0.9
etc
1/3 = 3 | 2/3 = 6 | 3/3 = 9
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He goes the other way, but if they are the same numbers: How can 9 equal to 10? Of course, if you went & bought something that costed 0.99, you obviously have to pay 1 for it. But that's not what the question is about, that's a question of what the numbers are worth which is irrelevant.
Oh, he also assumes that saying 0.99999 - 0.00001 is meaningless as the zeros goes on forever, it does indeed count as for each 9 is added, there's also one zero added (BEFORE the number 1 in the end).
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