The Instigator
mongeese
Con (against)
Winning
44 Points
The Contender
abard124
Pro (for)
Losing
39 Points

".99999...(repeating) is equal to 1"

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Voting Style: Open Point System: 7 Point
Started: 6/2/2009 Category: Miscellaneous
Updated: 7 years ago Status: Voting Period
Viewed: 1,537 times Debate No: 8515
Debate Rounds (3)
Comments (12)
Votes (13)

 

mongeese

Con

My opponent claimed the above in an earlier debate. PoeJoe called it an auto-win for him. I disagree.

I will allow my opponent to show how 0.9999(r) could possible be equal to 1.

Thank you for accepting this debate, should you accept.
abard124

Pro

.(9)=1---Part 2!

I would like to thank PoeJoe for bringing up the point that this is an auto-win, because he effectively instigated your challenge.

I won't dig too deep into this in the first round, but just to give you some ammo to work with, the simplest proof goes like this:

.(9)=?=1
/3 /3
.(3)=.(3)

Simple division property of equality proves it here. I'll save the slightly more complex proofs for later arguments.

Also, just a warning: When I debated this last time, my opponent used only empirical observations, and I think that hurt him, because you can't solely use empirical evidence when working with infinity, because infinity isn't a number, and it acts differently than numbers. you can use it to supplement your argument, but please do not use only empirical observations to "prove" your point.

Looking forward to your argument!
Debate Round No. 1
mongeese

Con

My opponent's first proof involves dividing both 0.9(r) and 1 by 3.
Now, when you divide 0.9(r) by 3, you truly do get 0.3(r).
However, when you divide 1 by 3, you get 1/3.
1/3 and 0.3(r) are not equal. It is impossible to truly convert a fraction that is not divisible by a factor or multiple of ten into a decimal. Decimals lose precision. The closest decimal we have to 1/3 is 0.3(r). However, they are not the exact same. This point is most easily clarified through empirical observations.
[0.9/3=3/10]
[0.99/3=33/100]
[0.999/3=333/1000]
[0.9999/3=3333/10000]
By this pattern:
[0.9999(r)/3=3333(r)/10000(r)]
However, any number that is just a series of threes divided by a power of ten does not simplify into 1/3. It gets closer every time, but it never reaches the end. It just can't. It would be oh so very close, but it won't be equal. It's an asymptote.

The simplest proof has simply been refuted. I await the next proof.

Thank you for accepting, by the way.
abard124

Pro

Every fraction in the world can be written as a perfect decimal. These decimals are what we know as rational numbers. Rational numbers either terminate or repeat. 1/3 cannot be written as a terminating decimal, so it has to repeat. And like you said, so does .(9)/3.

Also, like I said, empirical evidence doesn't really work with infinity. It works with numbers, but infinity isn't really a number, and it doesn't follow patterns. It's like the whole thing with an infinite number of monkeys and infinite typewriters, one would eventually write Shakespeare. The odds are so slim that if you had a reasonable number of monkeys, or even every monkey on earth, there's no way that one could crank out Shakespeare, but the moment you put infinity into the equation, that implies that every combination of characters will come out at least once. I know that that was a bit of a tangent, but I'm just trying to explain how infinity doesn't work the same as any number, and your empirical pattern is therefore null and void. I simply refuted your simple refutation of my simplest proof

But if you still don't like my first one, try this:

x=.(9)
10x=9.(9)
-x
9x=9
x=1

Here's another. It does rely on empirical observations, but it does not rely on patterns to infinity.

1/9=.(1)
2/9=.(2)
3/9=.(3)
4/9=.(4)
5/9=.(5)
6/9=.(6)
7/9=.(7)
8/9=.(8)
9/9=???

Based on the pattern, shouldn't it be .(9)? But wouldn't simple logic tell you that it's 1? Well, they're both right, because it's the same number.

Looking forward to your response!
Debate Round No. 2
mongeese

Con

http://www.merriam-webster.com...

Rational - involving only multiplication, division, addition, and subtraction and only a finite number of times

A rational number must be able to be a fraction. A rational number is not required to be able to be written as a decimal.

Your second proof was not used in the debate that I considered possible to win, which is what we are debating.

Finally, your third proof again assumes that all fractions must have decimal counterparts, which you have not shown to be true.
abard124

Pro

abard124 forfeited this round.
Debate Round No. 3
12 comments have been posted on this debate. Showing 1 through 10 records.
Posted by wjmelements 7 years ago
wjmelements
In light of recent vote bombings, I am reviewing many of mongeese's debates.

B/A: TIED
COND: CON (forfeits)
S/G: TIED (no major infractions)
ARG: CON (had real sources been used, this would go to that party. It was a "Yes it is" vs "No its not" debate with the frac/dec argument. The asymptote was more convincing to me and PRO had BOP.)
SRC: CON (1-0)
Posted by mongeese 7 years ago
mongeese
Failing to refute generally comes out of arguments, not conduct.
Oh, well. A conceded round usually decides it for me.
Posted by abard124 7 years ago
abard124
You're right about spelling and grammar, I was confusing it with the other debate on this same subject, which the spelling and grammar was not perfect; I changed that.

I'm not changing conduct, though. I would very much have liked to have been able to post that last round, but I wasn't. For that reason, I judge my debates, as well as any others, by the rounds that were actually there. You did not refute all of my proofs, and that is why I did not give you conduct.
Posted by mongeese 7 years ago
mongeese
So, you gave yourself conduct, after you forfeited a round?
And you gave yourself spelling and grammar? Did I make a grammar error?

I just want you to realize what you're doing with your vote, and how it may affect your reputation.
Posted by abard124 7 years ago
abard124
My bad...
I meant to tie the sources category...
Thanks for catching that (I suppose)...
Posted by mongeese 7 years ago
mongeese
I'm hoping that that vote against me isn't yours.
Posted by abard124 7 years ago
abard124
Terribly sorry about that last round...
Oh well, it just works against me, I suppose...
Posted by mongoose 7 years ago
mongoose
And he gets pwned by the proof that he knows works against him and he cannot refute... which brings up the question: why did he start this debate when he knew he was arguing the wrong answer???
Posted by mongeese 7 years ago
mongeese
Oh, yeah.
Posted by Maikuru 7 years ago
Maikuru
Hot off his 2+2=/=5 win, mongeese is set to debunk all mathematical tomfoolery.
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