Instigator / Pro
Points: 56

0.999... = 1

Finished

The voting period has ended

After 8 votes the winner is ...
Nemiroff
Debate details
Publication date
Last update
Category
Education
Time for argument
Three days
Voting system
Open voting
Voting period
One month
Point system
Four points
Rating mode
Rated
Characters per argument
10,000
Contender / Con
Points: 18
Description
No information
Round 1
Published:
How to convert a repeating decimal into a fraction: https://studymaths.co.uk/topics/convertingRecurringDecimalsToFractions.php

X = 0.333... 
10x = 3.333....
10x - x = 3.333... - 0.333...
9x = 3
X = 3/9 = 1/3
0.333...  = 1/3


X = 0.111...
10x = 1.111...
10x - x = 1.111... - 0.111...
9x = 1
X = 1/9
0.111... = 1/9

X = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
X = 9/9 = 1

Published:
Nonsense 1 is greater than anything less than one even by a bit
Round 2
Published:
1 is greater then anything less then 1, even by a bit. But 0.999... is clearly = to 1. And anything equal is not less then 1, even by a bit.

0.333 is not 1/3rd. 0.333333333 is not 1/3rd.
0.3 and any finite number of zeros is still less then 1/3rd. Even if there are billions of trailing 3's, still less then 1/3rd (even if by only a bit).
But 0.3 with *infinite* 3s is 1/3rd.
Just like 0.9 with *infinite* 9s is 1.

Your error lies in the fact that infinity is not a number. Infinity is not simply alot of 9s. Its never ending. To infinity. If 0.999... =/= 1, then 0.333... =/= 1/3, which it most certainly does.

And finally, appeals to logic are always weaker then objective fact, like a mathematical proof. Heres another proof:

0.333... = 1/3
0.333... (x3) = 1/3 (x3)
0.999... = 3/3 = 1
Published:
you are splitting hairs , literally!
Round 3
Published:
Disagree. This is not a question of semantics or anything like that. This is fact, as certain as 1 = 1.

I thought that 10x in my original formula was conveniently easy. If it is an iron fact rule, any multiplication of both sides of the equation should work.

First i tried 5, assuming wrongly that 5x would be half of 9.9999999.... as 4.5454545.... forgetting to carry remainders. If you punch in 0.99999 ×5 into a calculator you will get 4.99995. Add more 9s, the answer adds more 9s. No other changes. So assuming infinite 9s, 5x would be 4.99999.... and the final 5 would never come. Thus:

X = 0.999...
5x = 4.999...
5x - x = 4.999... - 0.999...
4x = 4
x= 4/4=1

Again with 3.

3x=2.999...
3x-x=2.999... - 0.999
2x=2
X=1

Again with 23
23x= 22.999...
22x=22
Forfeited
Added:
Unfortunately your video doesnt match your argument. The video uses my first proof at time stamp 1:50, and my second proof at 6:10. So not only does it support my conclusion, but also my methods.
Instigator
#106
Added:
Here's a video to explain it. .9999... is a number, not a real one. It explains basic calculus as well, as that's the method used to prove this.
https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/infinity/v/9-999-reasons-that-999-1
It explains that it is true, but requires more in depth math to truly understand and apply. What you said is true, but the methods aren't true.
Added:
--> @InFakeWars
I didnt forget that factor. I didnt say its infintely close to 1. I said it IS one.
Its also very much a real number, an official category with an official definition. Not only is 0.999... a real number, its a "rational" number, unlike pi, or square root of 2 which are "irrational numbers"
Infinity is not a number, but 9.999... is not infinity. It has infinite 9s after the decimal point, but it isnt itaelf infinity. How can a number smaller then 11 be infinity?
The math i used was math intended to be used for repeating decimals. Did you really read my arguments? Or are you offering to be a new challenger?
Instigator
#104
Added:
You forgot a key factor. A number infinitely close to 1 but isn't 1 is technically outside the real numbers category, therefore you can't convert it as could be done with normal mathematics. Yes, irrational numbers can be done so, but they are considered Real Numbers as well. .99999999999, forever, is NOT considered a, "real number." And therefore can not be simplified to one.
Infinity (which is the case with 9.99.....) is not considered a real number, as you can't add or subtract 1 from infinity. It's still infinity, regardless. There's no end to 9.99...... as the 9's can continue on forever. So, using math for real number's don't apply.
Added:
--> @Ragnar
I wish that were always true, especially in online debate channels :p Perhaps if i knew the person better.
Instigator
#102
Added:
--> @oromagi, @Nemiroff
Oromagi,
Thanks for clarifying.
Nemiroff,
You can probably still pull the point off just fine.
A good benchmark I look at, is if the words seem too absurd to be believed by the person stating them. As a hilarious example, the majority of this debate: https://www.debateart.com/debates/866/fetuses-as-a-replacement-for-the-usd
Added:
--> @oromagi
Well that settles that lol.
This does negate one of my arguments in another debate so thats vexing. Lol
Instigator
#100
Added:
--> @Nemiroff
My statement that he was engaging in sarcasm is an assumption, but one grounded in him not seeming to be insane elsewhere on this site. So I firmly believe he was saying "lazy" in jest, not expecting anyone to ever fill the entire universe with repeating decimal points. Were someone to hypothetically do so, there would be no room left for the existence of 1.00000...., all that would be left is 0.99999....
#99
Added:
--> @Ragnar, @Nemiroff
Just to confirm I was not genuinely criticizing PRO for failing to represent infinity in actual space-time, since that would break the universe I’m using presently. In truth, I am mostly pro-abstraction.
#98
Added:
--> @Ragnar
No, i do not.
Sarcasm is incredibly hard to convey through text, especially with no attempt to clearly convey it, and to someone who knows nothing about you. Furthermore his second paragraph explaining why he voted for pro with "nevertheless", a statement that supports the assertion that he is voting against his beliefs.
May i recommend either of: 😜,😋,🙃,👹,💩 or 😇 to denote sarcasm. Those who are not emoji-able can use the less technical :p
To be honest it seemed like yet another misunderstand of infinity. Not that ridiculous when 2 debators had already just made that mistake.
Instigator
#97
Added:
--> @Nemiroff
Saw you reference a vote here in a debate, and just to be clear, you know that was sarcasm right?
>>If PRO wasn't so lazy and instead took the time the fill the known universe with repeating nines it would be apparent to everybody that the integer 1 is quite different from the infinitely inexpressible .9999....
>Oromagi insisted that my claim was incorrect and that he could have done a better job (i disagree as my claim is a clear cut fact), but still voted for me based on the merit of my arguments.
#96
Added:
--> @oromagi
I can take your challenge if you like :D
Instigator
#95
Added:
Criterion Pro Tie Con Points
Better arguments ✔ ✗ ✗ 3 points
Better sources ✗ ✔ ✗ 2 points
Better spelling and grammar ✔ ✗ ✗ 1 point
Better conduct ✔ ✗ ✗ 1 point
Reason: I for one am totally unimpressed with this popular assertion- the only reason the math works is because PRO shorthands the infinitely repeating decimal point. If PRO wasn't so lazy and instead took the time the fill the known universe with repeating nines it would be apparent to everybody that the integer 1 is quite different from the infinitely inexpressible .9999....
Nevertheless, PRO did the math and backed his argument with citations. CON offered one assertion without any proofs and that was easily falsified in certain creative contexts. PRO made his case.
Grammar to PRO for CON's misuse of the adverb "literally" which means 'verbatim'- no metaphor should be here read. This VOTER scoured the debate for some reference to the division of follicles and finding none, failed to comprehend CON's intention or cohere this statement to implied thesis.
Conduct to PRO for CON's single forfeit
#94
Added:
--> @Virtuoso
I've re-voted, with an expansion on S&G.
As per the original vote... Since you think the quoted bit under S&G ("you are splitting hairs , literally!") was neither incoherent nor incomprehensible, would you please explain its connection to the concepts under discussion in this debate? To me it is self evidently not. Bare in mind, this is the entirety of a round I've copy/pasted.
#93
Added:
--> @PressF4Respect
*******************************************************************
>Reported Vote: PressF4Respect // Mod action: [Removed]
>Points Awarded: 7 points to pro
>Reason for Decision: See below
Reason for Mod Action>Reason for Mod Action: None of this RFD is sufficient per our standards. The voter fails to properly evaluate and weigh the points given. Please review the COC https://www.debateart.com/rules
******************************************************************
#92
#8
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
Pro was the only one to attempt an argument, and it was based on sound mathematics. Con did not really attempt to rebut, accused pro of 'spitting hairs,' and then forfeited.
#7
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
rFd In CoMmEnTz
#6
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
Arguments: Pro established a sound mathematical proof which supported his claim that 0.999... = 1. Con did not offer any proof to assert that this was not true, nor did Con offer any evidence to refute any of pro's arguments (the only thing Con said was "It's splitting hairs... literally!")
Conduct: Con forfeited final round
#5
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
See previous vote, with the following expansion to S&G (I stand by the original, but I am not against amending since two users had a problem):
Con had a complete absence of the correct punctuation, missing capitalization on gibberish sentences which seemed to be lacking at least their first parts, and more...
An important thing is that this is not a case of "one or two minor spelling mistakes." This is a case of the magnitude as a percentage of arguments. Con makes a case that there is "a bit" floating somewhere, but never attempts to be comprehensible by explaining where it is, or even what it is in terms of values (very important on a math debate). He even calls the very existence of the number one, nonsense: "Nonsense 1." With a comma in between, the term "nonsense" would be separate, thus referring maybe to pro's argument, instead of referring to the single most basic number in any counting system.
Con proceeds to proclaim that this debate was not about numbers at all, but about "hairs," which is incoherent already, but they were even more incoherently being "split" in some undefined 'literal' way never hinted at.
Remember, S&G is not just spelling, but grammar as well. If every one of your sentences make no sense in relation to anything else, there's a good chance the grammar of word choices have failed.
#4
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
1 arguments: pro presented a mathematical argument as to why 0.999r = 1, other than calling it nonsense, con did not offer an argument.
Conduct to pro for cons forfeit.
#3
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
Conduct: Forfeit
Arguments: Pro was the only one to really provide arguments for their side. Con's main argument was "Nonsense 1 is greater than anything less than one even by a bit." Pro countered this by using sound mathematical equations that prove that 0.999.... is, in fact, equal to one. Finally, con completely dropped pro's points. Con failed to respond to the mathematical equations provided, thus pro wins.
#2
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
Con forfeits 2 Rounds, laughs at his opponent 'splitting hairs' and clearly doesn't try at all. Thus, conduct to Pro.
Only Pro used sources, one helped clarify how to get decimals from fractions, the other helped verify that he is using a genuine, respected proof of 0.9r(ecurring) being equal to 1.
I want us to take note that 0.1r * 9 clearly is not equal to 1, just to make it clear why both equations abuse 10*variable and 9*variable situations and neither works backwards to get the other, between 0.9r and 1. Thus, I want it to be crystal clear that Pro is incorrect if we analyse the logic fully, I say this for the sake of clarifying that Con lost due to not trying, not due to the opponent having very strong arguments. Because Con's only arguments were that 1 can only be equal to 1 and that Pro is splitting hairs, without slightly touching on Pro's logic it therefore follows that Pro was handed the win.
#1
Criterion Pro Tie Con Points
Better arguments 3 points
Better sources 2 points
Better spelling and grammar 1 point
Better conduct 1 point
Reason:
Pro relays several equations that prove 0.999...=1. Con fails to demonstrate how this is false, merely saying that Pro is "splitting hairs", and 0.999... is smaller because it must be even if only by a small amount, con doesn't back this up with any equation and doesn't provide me with a single reason why I should believe him.
So nem is the only one to provide me with any evidence at all to support his case.
Conduct to pro because of cons forfeiture.