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Non Diving Posts: Discuss Bit of maths in the Non-Diving Related Forums forums: Apparently 0.999… (nought-point-nine recurring) is the same as 1. Not just very close, but precisely identical: a = 0.999… 10a ...

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Old 25-10-07, 06:08 PM
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Bit of maths
Apparently 0.999… (nought-point-nine recurring) is the same as 1. Not just very close, but precisely identical:

a = 0.999…
10a = 9.999…
10a - a = 9.999… - 0.999…
9a = 9
a = 1


Any mathematicians feel like explaining please do, cos it beats the hell out of me.
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Old 25-10-07, 06:18 PM
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Nope - 9a = 8.999999999999999999999999999999999r

Juz
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Old 25-10-07, 06:23 PM
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Quote:
Originally Posted by Juz
Nope - 9a = 8.999999999999999999999999999999999r

Juz
Hmm, it would do if you just multiply 0.9999... by 9. But where's the flaw in the working?
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Old 25-10-07, 06:28 PM
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Quote:
Originally Posted by Lazlo
a = 0.999…
10a = 9.999…
no: 10a = 9.99
Quote:
10a - a = 9.999… - 0.999…
9a = 9
a = 1
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Old 25-10-07, 06:32 PM
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9.9999999999999r minus 0.99999999999r

=

8.999999999999999r

Juz
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Old 25-10-07, 06:32 PM
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Quote:
Originally Posted by weazelz
no: 10a = 9.99
You've missed the "recurring" bit. It's not 0.999 it's 0.999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 999999999999999999999999999.........

etc
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Old 25-10-07, 06:32 PM
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Quote:
Originally Posted by Lazlo
Apparently 0.999… (nought-point-nine recurring) is the same as 1. Not just very close, but precisely identical:

a = 0.999…
10a = 9.999…
10a - a = 9.999… - 0.999…
9a = 9
a = 1


Any mathematicians feel like explaining please do, cos it beats the hell out of me.
Hang on a minute. .... You're actually using 0.999 here NOT 0.9 recurring

So ...
a = 0.999 .................. OK
10a = 9.999… NO, 10a = 9.990
Therefore
10a - a = 9.990 - 0.999
which actually equals 8.991
So
9a = actually equals 8.991
Therefore
a = 8.991/9
a = 0.999 ................ As it should

If you have a calculator with a proper 'pure' recurring function things might be different. Dunno, I'm not a mathematician
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Old 25-10-07, 06:34 PM
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Quote:
Originally Posted by Lazlo
You've missed the "recurring" bit. It's not 0.999 it's 0.999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 999999999999999999999999999.........

etc
Yeah, but then 10a would equal 9.999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999
wouldn't it and there is always the 0.111111111111111111111111111111111111111111111111 11111111111111 to consider
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  #9 (permalink)  
Old 25-10-07, 06:37 PM
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Quote:
Originally Posted by Sixsquid
Hang on a minute. .... You're actually using 0.999 here NOT 0.9 recurring

So ...
a = 0.999 .................. OK
10a = 9.999… NO, 10a = 9.990
Therefore
10a - a = 9.990 - 0.999
which actually equals 8.991
So
9a = actually equals 8.991
Therefore
a = 8.991/9
a = 0.999 ................ As it should

If you have a calculator with a proper 'pure' recurring function things might be different. Dunno, I'm not a mathematician
Now you've missed the recurring bit as well!

10 multiplied by 0.9 recurring is 9.9 recurring.

I'm still thinking about Juz's last answer...
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  #10 (permalink)  
Old 25-10-07, 06:38 PM
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Quote:
Originally Posted by Sixsquid
Yeah, but then 10a would equal 9.999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999
wouldn't it and there is always the 0.111111111111111111111111111111111111111111111111 11111111111111 to consider
Errrr....
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