.99 Repeating = 1

I_Gorged_Your_Mom · June 2004

. <u>99</u> = 1

Swiftspear · June 2004

Only if you're not trucating <img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' />

OttoDestruct · June 2004

int number = 0.99;

Doesn't work.

Caboose · June 2004

<u>.99</u> = <u>.99</u>

plain and simple. It is as close to being 1 as you can get without being 1, but it's not 1.

Cereal_KillR · June 2004

0.99999999 going to infinity IS = 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.

I_Gorged_Your_Mom · June 2004

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

OttoDestruct · June 2004

</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'> 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  </td></tr></table><div class='postcolor'> 
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that.

Ratonetwothreetwoone · June 2004

i dont think i belong in here

/me backs out slowly

I_Gorged_Your_Mom · June 2004

go ahead and try

Cereal_KillR · June 2004

</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'> </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'> 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 </td></tr></table><div class='postcolor'>
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that.  </td></tr></table><div class='postcolor'> 
no you can't. One is mathematically correct, the other wouldn't be. <img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' />

NumbersNotFound · June 2004

1/3rd = .3333333333333333
2/3rds = .666666666666666
3/3rds = .999999999999999

UnderDOG · June 2004

.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.

I_Gorged_Your_Mom · June 2004

so then everyone here must agree that .<u>99</u>=1.

DOOManiac · June 2004

Anything between .9999 and 1 is = 1. Otherwise you have too much time on your hands to worry about that sort of crap. Go do something. :P

BlackMage · June 2004

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

[WHO]Them · June 2004

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.

BlackMage · June 2004

</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'> 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.  </td></tr></table><div class='postcolor'> 
that's what i said, but less algebraic

Surge · June 2004

</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'> . <u>99</u> = 1 </td></tr></table><div class='postcolor'>
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]Them · June 2004

</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'>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</td></tr></table><div class='postcolor'>
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.

7Bistromath · June 2004

[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.

Jefe · June 2004

</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'> 3. subtract x from the left, 0.9 repeating
from the right, giving

9x = 9  </td></tr></table><div class='postcolor'> 
Can you find what's wrong with this picture?

Mantrid · June 2004

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.

Jefe · June 2004

</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'> </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'> </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'> 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 </td></tr></table><div class='postcolor'>
If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. </td></tr></table><div class='postcolor'>
no you can't. One is mathematically correct, the other wouldn't be. <img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' />  </td></tr></table><div class='postcolor'> 
Yes you can.

Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS

POOP_Akira · June 2004

Umm... Whats a 9?

*head explodes*

I_Gorged_Your_Mom · June 2004

You have to devide them both by the same number, not one 21411513515 and they other 1.

In the proof, x= .<u>99</u>

Soylent_green · June 2004

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'>
Yes you can.

Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS</td></tr></table><div class='postcolor'>

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.

Cold_NiTe · June 2004

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO)</td></tr><tr><td id='QUOTE'>Them,Jun 19 2004, 08:36 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'>
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
</td></tr></table><div class='postcolor'>
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. </td></tr></table><div class='postcolor'>
I think [WHO]Them has got you there Gorged.

This being the most important part:
</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'>3. 10N - N = (10 - 10S) - (1 - S)
9N = 9 - 9S

4. N = 1 - S
5-6. N = N</td></tr></table><div class='postcolor'>

I don't think you can do this as well:
</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'>3. subtract x from the left, 0.9 repeating
from the right, giving</td></tr></table><div class='postcolor'>
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.

B33F · June 2004

Think like a lazy engineer: .9 is close enough to 1.

<a href='http://www.phy.ilstu.edu/~rfm/EPMjokes.html' target='_blank'>http://www.phy.ilstu.edu/~rfm/EPMjokes.html</a>

pardzh · June 2004

OH GOD IT'S MATH RUN FOR YOUR LIVES!

ZiGGY · June 2004

.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.

[WHO]Them · June 2004

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (ZiGGY^ @ Jun 19 2004, 08:02 PM)</td></tr><tr><td id='QUOTE'> .9 recurring infinite decimal is 1, it is by definition  </td></tr></table><div class='postcolor'> 
Got a link?

.99 Repeating = 1

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