Only if you're not trucating <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
edit: this is considering you are going all the way to infinity and never stopping. This is due to the fact there is no "last decimal." This cannot be done by a computer which actually goes really far but still stops at a given point.
<!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1
[proof follows below]
1. let x = 0.9 repeating 2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating 6. therefore
0.9 repeating = 1 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that.
<!--QuoteBegin-OttoDestruct+Jun 20 2004, 02:22 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (OttoDestruct @ Jun 20 2004, 02:22 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1
[proof follows below]
1. let x = 0.9 repeating 2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating 6. therefore
0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
.99 repeating an infite number of times is technicly one, but if you ever stop, and there is a definative number of nines, then it no longer equals one.
0.33333333333333 (off to infinity) is close to 1/3 0.66666666666666 (off to infinity) is close to 2/3 0.99999999999999 (off to infinity) is close to 3/3 and close to 1
you forget one thing, 0.<u>333</u> is unattainable by the defenition of infinity and can only be defined as 1/3
<!--QuoteBegin-[WHO]Them+Jun 19 2004, 07:59 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO]Them @ Jun 19 2004, 07:59 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> You can't do such a simplistic proof on an infinite quantity, the math simply breaks down.
It's the same concept as a limit, you never actually get to 1, just really... reallly.... really close.
0.9999.... is a concept, not a real number. The same as infinity is a concept. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> that's what i said, but less algebraic
<!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 11:13 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 11:13 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> . <u>99</u> = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> That's incorrect. That's like saying pi = 3.14159265, which is incorrect. Pi = Pi. Like how you can't write the square root of 2 accurately. Accurately, the square root of 2 is the square root of 2.
[WHO]ThemYou can call me DaveJoin Date: 2002-12-11Member: 10593Members, Constellation
<!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 05:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 05:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->To prove: 0.9 repeating = 1
[proof follows below]
1. let x = 0.9 repeating 2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating 6. therefore
0.9 repeating = 1<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> I'm bored, so here's your counter-proof (I finally get to put my group theory studies to use, w00t)
If you plan to create your own field (in the group theory sense of the term), then what you said totally works. But In the real number field that most the rest of the world uses, every number has an additive inverse. Since you fail to explicitly define your conceptual number, we'll need to implicitly define it's additive inverse...
Let N be your conceptual number 0.<u>99999</u> Let S be N's additive inverse.
S <i><b>must</b></i> satisfy the following property.... N + S = 1
So, let's rewrite your proof a bit so that it actually makes some sense.
[WHO]Them should go to the Constie forum more often so he can free us from the oppressive .<u>99</u>=1ish-ness of the great and terrible I Gorged Your Mom.
<!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 06:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 06:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> 3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Can you find what's wrong with this picture?
The whole .99... = 1 phenomenon is more of a philosophical matter rather than an algebraic, mainly because it forces you to try and accept two things that are mutually exclusive and yet both true at the same time. It also deals with a metaphysical aspect in that something incomplete is the same as a whole.
<!--QuoteBegin-Cereal_KillR+Jun 19 2004, 06:25 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Cereal_KillR @ Jun 19 2004, 06:25 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-OttoDestruct+Jun 20 2004, 02:22 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (OttoDestruct @ Jun 20 2004, 02:22 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1
[proof follows below]
1. let x = 0.9 repeating 2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating 6. therefore
0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Yes you can.
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
He isn't using circular logic, you are. He first defines x = 0.9999..., this is not what he is trying to prove. You can allways multiply, divide, add or subtract a number from both sides if you wish, this changes nothing if they are equal, and per definition we know x = 0.999.... . If you try to emulate his proof(which among others [who]them has allready showed isn't water tight due to other subtleties with infinites) you get this:
<!--QuoteBegin-[WHO+--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->Them,Jun 19 2004, 08:36 PM] <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 05:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 05:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> 1. let x = 0.9 repeating 2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating from the right, giving
9x = 9
4. divide both by nine, giving
x = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> Let N be your conceptual number 0.<u>99999</u> Let S be N's additive inverse.
S <i><b>must</b></i> satisfy the following property.... N + S = 1
So, let's rewrite your proof a bit so that it actually makes some sense.
Learned nothing, gained nothing. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> I think [WHO]Them has got you there Gorged.
This being the most important part: <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. 10N - N = (10 - 10S) - (1 - S) 9N = 9 - 9S
4. N = 1 - S 5-6. N = N<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I don't think you can do this as well: <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. subtract x from the left, 0.9 repeating from the right, giving<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> Mathmatically, you can't interchange the variable if the variable is what you are proving, I think... Hmm I'm not so certain now. Oh well, you get the idea.
.9 recurring infinite decimal is 1, it is by definition and it is by reason a part of infinite decimal systems, dont argue it any other way they are the same.
Comments
Doesn't work.
plain and simple. It is as close to being 1 as you can get without being 1, but it's not 1.
seeing as how 10x 0.99999999 = 9.99999999 (all going to infinity)
9x 0.99999999 = 10x 0.99999999 - 0.99999999
9x 0.99999999 = 9.99999999 - 0.99999999
9x 0.99999999 = 9
0.99999999 = 1
edit: this is considering you are going all the way to infinity and never stopping. This is due to the fact there is no "last decimal."
This cannot be done by a computer which actually goes really far but still stops at a given point.
[proof follows below]
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating
6. therefore
0.9 repeating = 1
[proof follows below]
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating
6. therefore
0.9 repeating = 1 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that.
/me backs out slowly
[proof follows below]
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating
6. therefore
0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
2/3rds = .666666666666666
3/3rds = .999999999999999
0.66666666666666 (off to infinity) is close to 2/3
0.99999999999999 (off to infinity) is close to 3/3 and close to 1
you forget one thing, 0.<u>333</u> is unattainable by the defenition of infinity and can only be defined as 1/3
It's the same concept as a limit, you never actually get to 1, just really... reallly.... really close.
0.9999.... is a concept, not a real number. The same as infinity is a concept.
It's the same concept as a limit, you never actually get to 1, just really... reallly.... really close.
0.9999.... is a concept, not a real number. The same as infinity is a concept. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
that's what i said, but less algebraic
That's incorrect. That's like saying pi = 3.14159265, which is incorrect. Pi = Pi. Like how you can't write the square root of 2 accurately. Accurately, the square root of 2 is the square root of 2.
[proof follows below]
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating
6. therefore
0.9 repeating = 1<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I'm bored, so here's your counter-proof (I finally get to put my group theory studies to use, w00t)
If you plan to create your own field (in the group theory sense of the term), then what you said totally works. But In the real number field that most the rest of the world uses, every number has an additive inverse. Since you fail to explicitly define your conceptual number, we'll need to implicitly define it's additive inverse...
Let N be your conceptual number 0.<u>99999</u>
Let S be N's additive inverse.
S <i><b>must</b></i> satisfy the following property.... N + S = 1
So, let's rewrite your proof a bit so that it actually makes some sense.
1. N = (1 - S)
2. 10(N) = 10(1 - S)
10N = 10 - 10S
3. 10N - N = (10 - 10S) - (1 - S)
9N = 9 - 9S
4. N = 1 - S
5-6. N = N
Learned nothing, gained nothing.
from the right, giving
9x = 9 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
Can you find what's wrong with this picture?
[proof follows below]
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
5. yet x = 0.9 repeating
6. therefore
0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
Yes you can.
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS
*head explodes*
In the proof, x= .<u>99</u>
Yes you can.
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
He isn't using circular logic, you are. He first defines x = 0.9999..., this is not what he is trying to prove. You can allways multiply, divide, add or subtract a number from both sides if you wish, this changes nothing if they are equal, and per definition we know x = 0.999.... . If you try to emulate his proof(which among others [who]them has allready showed isn't water tight due to other subtleties with infinites) you get this:
<i>2.</i> 10x = 10(8933490320 + 9040340348993488934983498)
<i>3.</i> 9x = 9(8933490320 + 9040340348993488934983498)
<i>4.</i> x = 8933490320 + 9040340348993488934983498
<i>5.</i> yet x = 8933490320 + 9040340348993488934983498
<i>6.</i> therefor 8933490320 + 9040340348993488934983498 = 8933490320 + 9040340348993488934983498
So, you proved nothing and your back where you started unless you use an infinitely repeating decimal number.
1. let x = 0.9 repeating
2. multiply each side by ten, giving
10x = 9.9 repeating
3. subtract x from the left, 0.9 repeating
from the right, giving
9x = 9
4. divide both by nine, giving
x = 1
<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Let N be your conceptual number 0.<u>99999</u>
Let S be N's additive inverse.
S <i><b>must</b></i> satisfy the following property.... N + S = 1
So, let's rewrite your proof a bit so that it actually makes some sense.
1. N = (1 - S)
2. 10(N) = 10(1 - S)
10N = 10 - 10S
3. 10N - N = (10 - 10S) - (1 - S)
9N = 9 - 9S
4. N = 1 - S
5-6. N = N
Learned nothing, gained nothing. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I think [WHO]Them has got you there Gorged.
This being the most important part:
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. 10N - N = (10 - 10S) - (1 - S)
9N = 9 - 9S
4. N = 1 - S
5-6. N = N<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I don't think you can do this as well:
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. subtract x from the left, 0.9 repeating
from the right, giving<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Mathmatically, you can't interchange the variable if the variable is what you are proving, I think... Hmm I'm not so certain now. Oh well, you get the idea.
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