Instigator
Points: 35

0.999... = 1

Voting

The participant who scores the most points is declared the winner

The voting period will end in:
00:00:00:00
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
Points: 10
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:
--> @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
Added:
--> @PressF4Respect
Con dropped all points that pro made, and didn't try to counter any of pro's arguments at all.
Con did not provide any sources, either.
Slight edge to Pro for spelling + grammar as well.
Con also forfeited last round, which is poor conduct
#91
Added:
--> @Ragnar
*******************************************************************
>Reported Vote: Ragnar// Mod action: [Removed]
>Points Awarded: 7 points to pro
>Reason for Decision: See below
Reason for Mod Action>Reason for Mod Action: This RFD is fine except for the spelling and grammar point.
In order to award spelling and grammar (S&G) points, a voter must explicitly, and in the text of their RFD, perform the following tasks:
Give specific examples of S&G errors
Explain how these errors were excessive
Compare each debater's S&G from the debate
S&G errors are considered excessive when they render arguments incoherent or incomprehensible.
Although the voter did compare the grammar with the other side, ragnar did not explain why it was excessive and rendered the arguments incoherent or incomprehensible. It's not enough to vote for grammar for one or two minor spelling mistakes.
*******************************************************************
https://www.debateart.com/debates/1392/comment_links/19718
#90
Added:
--> @Ragnar
For this, let X=0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...
Arguments:
Pro showed with examples of mathematical proof that X is verifiably not less than 1. Con counters that 1 is greater than anything less than 1, but failed to in any way even try to connect this to X (if X is less than 1 by some bit, he needs to show that bit existing; whereas con showed that there is no last decimal place for the missing 0.00000000000000000000000000...1 to occur).
Sources:
So the Brit site StudyMath.co.uk bolstered that pro's proofs were valid, and Wikipedia that it was sound, due to people having worked this out long ago.
Con offered nothing, not even a challenege against the authority of that third party verification of pro's case (it's pretty essential on a debate like this, so the absence of it hurts more than the normal dropping of sources).
S&G:
Missing punctuation, capitalization, etc. Here's a gem (pasting a whole round here...): "you are splitting hairs , literally!"
Pro on the other hand was perfectly legible.
Conduct:
Forfeiture from con, no issues from pro.
Offered neg case:
There are two ways con could have conceivably won...
1. Argue that pro is launching a truism, which would make this an unmoderated troll debate.
2. Use the ≈ to demonstrate that while X is effectively 1, it is more true to say that X≈1 than to say X=1. ... Before reading this debate, that would have been my case, but I am now convinced (so it would have been a losing argument to me due to pro's argumentation skill, but it would have been a valid if unsound argument to make, which truly could have turned other voters... and yes, if well argued I could have voted in favor of it even while now disagreeing).
3. As a bonus I would have rejected offhand, a Kritik against our number system for not really existing such as the lengthy one carried out in the comment section. A slightly better one can be found within a single post here:
#89
Added:
--> @OoDart
*******************************************************************
>Reported Vote: OoDart// Mod action: [Removed]
>Points Awarded: 7 points to pro
>Reason for Decision:
I think 0.999 does not equal 1, and believe I could've put up a better debate. That being said, the Instigator by far won this debate, because they actually used legitimate arguments, unlike the contender.
Reason for Mod Action>Reason for Mod Action: This vote is not eligible to vote. In order to vote, an account must: (1) Read the site’s COC AND have completed 2 non-troll/non-FF debate OR have 100 forum posts.
*******************************************************************
#88
Added:
"Only a number that ends and reaches its endpoint can be deemed an actual number that exists."
This is a made up requirement for numbers.
https://www.mathsisfun.com/sets/number-types.html
Repeating decimals are not only "real numbers", they are ine of the broadest categories. Rational numbers. You made up an arbitrary definition and then got mad...
Instigator
#87
Added:
--> @Nemiroff
I have had enough of your bullshit, welcome to the blocklist.
#86
Added:
--> @RationalMadman
Are you making up definitions?
Instigator
#85
Added:
--> @Nemiroff
So, if it's an endless series of 9's then it can't be a number according to your logic.
Only a number that ends and reaches its endpoint can be deemed an actual number that exists. If 0.9 never reaches the last 9, it doesn't exist. 1.0 exists as an actual number the ends and has nothing left to 'reach' other than endless 'nothingness' which is infinite 0's. Therefore, 1.0 is an actual number and value while 0.9r0 is as bullshit of a joke as is the 0.0r1 that differentiates it from 1.0r0
#84
Added:
--> @RationalMadman
*there is no 9 at the end of the 9s*
Its just an endless series of 9s
Just like the endless series of days til you get your million.
There is no day that you miss your payment. There is nothing at the end of and *END*LESS series.
End-less. No-end. Infinity.
Instigator
#83
Added:
--> @Nemiroff
So because the number following all the 9s, is a 9, you carefully dodge needing to admit that 0.9r is impossible and can't exist. On the other hand, you happily point out that the 1 following the 0's can't exist in the difference between 0.9r9 and 1.0r0
#82
Added:
--> @RationalMadman
If i promise to pay you a million dollars, just wait an infinite amount of days before you get it... will the time ever come for you to get paid?
No you will never get paid. This promise may as well not exist.
Similarly your 1 at the end of infinite 0s may as well not exist. Thus the difference is 0.00..., or 0. And if there is no difference, they are the same.
Thank you for providing me with a suprising extra proof.
Instigator
#81
Added:
forfeits 1 round*** not 2, rest of my RFD is valid
#80
Added:
--> @Virtuoso, @bsh1
https://www.debateart.com/debates/1392/vote_links/3501
I am reporting Ragnar's vote solely for the S&G part of it.
#79
#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.