The Instigator
AKMath
Pro (for)
Losing
0 Points
The Contender
Percivil
Con (against)
Winning
3 Points

0.999... = 1 | Prove Me Wrong

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after 1 vote the winner is...
Percivil
Voting Style: Open Point System: 7 Point
Started: 6/13/2018 Category: Education
Updated: 4 months ago Status: Post Voting Period
Viewed: 466 times Debate No: 115532
Debate Rounds (5)
Comments (7)
Votes (1)

 

AKMath

Pro

0.999... = 1 | Prove Me Wrong
Percivil

Con

0.99999......when you round it off yes I agree it is equal to 1. But if you look at the bigger picture,0.999999.....is missing a 0.00000........01 to be added so that it becomes 1. Hence 0.99999999..... is NOT equal to 1
Debate Round No. 1
AKMath

Pro

Here are just a few examples why, I'd like to see you try disprove these ones:
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Between 1 and 2 there are infinite numbers. If two numbers/values are different they will always have a difference of something. So my question is: What number is in between 0.999... and 1?
Percivil

Con

Well 0.999999....doesnt stop but then again theres a missing .1 somewhere. If we round 0.999999.....to 3 decimal places it would be 0.999. For 0.999 to become 1,the number needs to be added with a 0.001. So although 0.999...doesnt stop,you just need to round it off to a certain number of decimal places for lets say 3 decimal places and add a 0.001 from there on.

To correct you:3/3 or 3 divided by 3=1 not 0.99999 as 3/3 is one whole. You can check with your calculator. I checked with mine,its 1 not 0.999999.... If it was 0.999999.... it would have shown 0.99999... like how 2/3 is shown as 0.66666667. Now wait yes they rounded the number off but if you mentally divide it,why do you think the answer is 1 instead of 0.999999.....? And when you divide the numbers,why do you not have any decimals to round off your answer to 1?

Question for my opponent:If 0.99999........=1, why do we call it 0.999999..... instead of 1?
Debate Round No. 2
AKMath

Pro

That"s a pretty dumb argument. A calculator obviously says 3 divided by 3 equals one. A calculator would not say 3 divided by 3 equals 2/2, 3/3, etc. 0.999... is simply just another way of saying 1. A calculator shows the simplest form of the answer. Why do we call it 0.999..., 0.999... instead of 1. 2/2 is 1 but it is still said as two halves or one. And, yes you could technically pronounce 0.999... as 1, just like people say 3/3 is 1. We don"t call 0.999... 1 because not enough people even know about this.
Percivil

Con

6 divided by 6=1
Simplify that it would be:
3 divided by 3 which is also equal to 1
OR
1 divided by 1=1
1x3=3
3 divided by 3 is one.

If you do long division, why is 3 divided by 3 1 and not 0.9999999.....?
Debate Round No. 3
AKMath

Pro

NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!
I didn't mean simplify the equation I meant simplify the answer.
When you divide 6 by 6/ 3 by 3, you do in fact get one. I'm saying that 0.999... is 1. You wouldn't say 6 divided by 6 equals three thirds. 1 and 0.999... are interchangable. And you have not disproved any of my proofs from round 2.

https://www.youtube.com...
Percivil

Con

Unless you"re telling me my math tutor is wrong,he"a saying your method is wrong. You said 0.99999....x10X=9.999999 so 9X=9.999999....-0.9999999....=9. So 0.9999999x9 should be equal to 9 right? Then why is it that my calculator showed me 8.9999999...instead of 9?
Debate Round No. 4
AKMath

Pro

Yes your math tutor is wrong. My method is in fact right. Look again why is it so complicated. I'll annotate it this time.

x = 0.999...
10x = 9.999... - If you multiply a decimal by 10 you simply move the decimal pint one spot to the right.
10x - x = 9.999... - 0.999... - Then you subtract x from 10x/ 9.999... - 0.999...
9x = 9
x = 1
Show your tutor my other two methods too. You still have not disproved any of them or showed me how they are wrong.
Your calculator showed it too you wrong as you put the equation into the calculator wrong. What does 0.999...x = 9.999... mean?
I think I have definitely proven 0.999... = 1.
Percivil

Con

I rounded the number to five significant figures so its 0.99999. If X=0.99999,by right you said the answer should be 9. If so why does it say 8.999991 on my calculator? It doesnt match. So your method is wrong. My 9X and your 9X is totally different.
To explain further:
Oppoents method:
X=0.99999(rounded it to 5 significant figures)
10X=9.9999
9X=9.9999-0.99999
=9

Flaw:9.99999-0.99999=8.999991

Hence my opponent"s method is wrong. Go check with your calculator.
Debate Round No. 5
7 comments have been posted on this debate. Showing 1 through 7 records.
Posted by Masterful 4 months ago
Masterful
Does 0.999=1? No because there is a difference of 0.001
Does 0.99999999999999=1? Nope, we face the same problem.
When does a string of 0.9s ever = 1? For every 0.9 you add you created a difference of 0.1 between the 0.9s and 1.

I could sit here for an infinite amount of time typing 0.999999999999.. and I would never hit the value 1.

You can only hit the value of 1 when you use a false representative of infinity such as 0.999.. this of course is not true infinity because true infinity is not real.
Posted by Masterful 4 months ago
Masterful
The third fallacy you have made is, when trying to identify what 9X is, you use a sum where you try to do infinity minus infinity.
"9.999..-0.999.." This is the flaw in your sum.

You've concluded that infinity minus infinity is 0, this is wrong

Infinity - Infinity = Undefined.

https://www.philforhumanity.com...
Posted by Masterful 4 months ago
Masterful
The second fallacy you have made is misunderstanding the concept of infinity and over simplifying it.

For 0.999.. to exist we would have to create decimal places infinitely small, so the question posed here is; what's the difference between infinitely small and simply not existing? There is no difference, this tells us that infinity is either undefined or impossible.
Posted by Masterful 4 months ago
Masterful
First off all I'd like to begin with this. To assert 0.999..=1 you must assume 0.001.. does not exist.
That's the first fallacy.
Posted by Masterful 4 months ago
Masterful
May I retract my previous comment as I was trying to prove that 0.88 can never become 0.89 but miss typed. I will continue to show your ignorance AKMath.
Posted by Masterful 4 months ago
Masterful
X=0.88
10X=8.8
8X=8
X=1

ALMath, Get rekkt by a math casual you noob. If I had debated you on this you'd die.
Posted by Masterful 4 months ago
Masterful
If we have infinite numbers, then the difference between 0.9999.. and 1 is infinite.
1 votes has been placed for this debate.
Vote Placed by RMTheSupreme 4 months ago
RMTheSupreme
AKMathPercivilTied
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Total points awarded:03 
Reasons for voting decision: AKMath doesn't explain why, if you do long division and divide 3 by 3 it never gets to 0.9 recurring. Con wasn't strong in this debate and should instead have done the argument in reverse. 0.9 recurring multiplied by 3 is 2.9 recurring (approaching a 7 at the end of the infinite 9's) and not actually 3 but even with con's weaker, passive style of debating he achieved it by reversing the angle to make Pro need to explain why the answer of 3/3 is never 0.9 recurring.