0.999 repeating equals 1

…I’m honestly having trouble understanding the question. The relevance of a given source to the debate and, often as a result, to source points isn’t something that we as moderators would determine, so whether you’d make that call is up to you.

Is a source backfiring on a sideproof barely relevant to the Con case enough to sway Sources in a debate that is not very source reliant like this?

Okay well I'd rethink my vote then. I read that too fast.

I did say that

"CON doesn't point out that his/her source says that the conclusion is both invalid and fallacious because it uses the divide by zero operation in the wrong way (anything divided by zero is undefined)"

If you are curious about what Pro should have said to Con's Round 2 proof:

(0 x 1) / 0 = (0 x 2) / 0

This is completely impossible, you cannot divide by 0 in the first place. At this point the proof is actually wrong both mathematically and logically.

Pro also could have completely won Sources point allocation had the erroenous posting of 'division by zero' Wikipedia that itself thwarts Con's trickery been shown to be a backfiring source by Pro in Round 3.

RFD PART 1/2

Pro's main argument that Pro says was not addressed by Con was the most heavily addressed argument by Con in the entire debate. For Pro to still in Round 3 conclude that Con didn't address the 0.333... argument is serious reading comprehension issues. On the other hand, the explanation Con gave to address it actually does fall short and I will explain specifically why.

Con's argument is that if you divide 1 by 3, it is not actually 0.333... it is 0.333... with an infinitesmally small (or minute) value above it. It would have actually helped if Con went further and pointed out it cannot exist because the very value above 0.333... that 1/3 is, literally doesn't exist and that is the very reason 1/3 of 1 can't be expressed numerically in the first place. That said, Pro's reply to it are all very cagey and defensive but they still do hold some value.

Pro replies that they themselves never explicitly stated rounding occured and that Con has to prove it. Con explained how if you multiply 0.333... by 3 you actually get 0.999... and not 1.000... ONLY IN THE LAST ROUND and even goes further to explore 1.0000...1 etc. This was definitely too late to qualify as a genuine argument as it is the final Round and on top of being the final Round, Con is the last debater to present their case, meaning Pro can't have an opportunity to rebuke it.

The biggest issue I have with Con's way of explaining 0.333... isn't 1/3 is that it keeps being stated as a self-evident truth.

Con actually backfires their entire argument by trying to prove trickier in mathematics without realising Pro can win the entire debate if Pro doesn't fight the trickery or proves it's a different format of trickery.

Let me explain.

Con ends Round 2 with this:
Here’s also this quick little thing:

0 x 1 = 0
0 x 2 = 0

Therefore,

0 x 1 = 0 x 2

And

(0 x 1) / 0 = (0 x 2) / 0

Which simplifies to

0/0 x 1 = 0/0 x 2

And then

1 = 2

Math is weird, yo.

Pro can do either of 3 things now:

1) Ignore it entirely, implicitly agreeing with the trickery (so 0.999... = 1 = 2) and let Con fight their own trickery in the last Round.
2) Explicitly agree with it for a troll angle and say, okay sure Con gets that, now they all can equal each other unless Con proves 1 doesn't equal 2 which is irrelevant to the debate.
3) Prove the form of tricky mathematics is different because for instance 0 is such a unique value unlike any other in mathematics etc.

Pro opted for option 1. To be honest, If Con had brought up the mathematics trickery in Round 1, I'd give it more weight as it becomes central to the debate. To randomly put it before the final Round is fine, that's still legitimate but that implies to me that Con was just illustrating trickery rather than wanting Pro to directly need to address it.

RFD PART 2/2

I also want to note that Con keeps lacking explanations.

".333… is only approximately equal to 1/3, because there will always be an infinitesimally small amount that will be needed to make.333… equal to 1/3, just as there will always be an infinitesimally small amount that will need to be added to .999… in order for it to be equal to 1.

This is why you get strange properties with numbers, such as 1/3 * 3 = 1, but .333…*3 = .999…
They are not the same value. But, for the sake of simplicity, we say that 1/3 * 3 = .333… *3, even though it does do not."

What is the purpose of not pointing out that 1/3 is unattainable or impossible? Con never explicitly points this out, instead it is said that there is a value equal to 1/3 above 0.333.... but the real point Con should have made is there is no value equal to 1/3 in denary mathematics (which is the 1-9 counting system that essentially all humans use for mathematical calculations). In a 1-5 system, where 6 becomes their 10, that senary system as opposed to the denary one we use could easier obtain 1.3 as an actual numerical value potentially (not important to my RFD to reveal it, I can tell you it's a simple enough value).

In fact the word 'denary' or the concept of the limitations of denary mathematics enabling Pro's trickery to present falsehoods as truths doesn't come up once in Con's argumentation. This is not me violating tabula rasa, I am not penalising Con for missing this out, I am finding it peculiar because to not even mention that 1/3 literally is unobtainable in denary counting systems while mentioning what Pro did, seems so peculiar to me.

Pro retorts as follows:

"If .333... is approximately equal to 1/3 I must have rounded somewhere in my proof to determine their exact equality, and CON should be able to point that out easily.
This is not the case as .333... or .999.... as they are exactly equal. CON did now show anywhere I have rounded, therefore, the argument is moot."

Which wouldn't work against me in Con's shoes, I would never have allowed it to get there. Con only had to take it one step further and explain that 1/3 doesn't exist in denary counting system.

What Con said was that 1/3 is falsely stated to be 0.333.... because there is an infinitesmally small 1/3 to add on top. This sounds correct but it is not correct. If the 1/3 to add on top is also 0.333... (which if you follow Pro's logic and mathematics, it would be) that will be 0.3333... ANYWAY.

As for this 'congruence' and such, I feel both sides got sidetracked there and I don't really feel Con proved Pro used sourcing poorly. Pro never used the term 'congruence' when Con pointed out the error... CON DID. It is Con who started bringing up 'congruence' which is only applicable to geometry and applying to pure mathematics that had no relevant to geometry that I could see.

I would accept that Con successfully threw doubt on the 10x-x proof but again, Con's trickery at the end of Round 2 completely backfires on Con. If Con is conceding that mathematics is flawed and that paradoxes can function inside of mathematics even though they shouldn't that SUPPORTS Pro being able to prove that 0.999.... = 1 even though it's paradoxical in other ways.

I am just tagging some people to vote because time is running out.
Please vote!

Please vote. Time is running out and I can't have another unovted tie

please vote

The biggest issue for me is both sides are correct.

Pro is correct if we stay within practical mathematical limitations. Con is correct if we deal with raw values and theoretically perfect mathematics.

This topic can be particularly hard to garner votes.

Imagine trying to read the exact same proofs for the dozenth time, while excluding previous insight from your rulings on it.

Please Vote!

I gotcha, thanks for the heads up. I think I only used one curse word in this debate, but I'm not used to this more official set up.

Too many can distract from the arguments, especially with how they tend to be aimed (at the person one is arguing against, instead of as part of a logical argument to the topic). It does of course take a lot.

More at:
https://info.debateart.com/terms-of-service/voting-policy#conduct

I can't use curse words? Damn.

1. 333...is just another way of writing 1/3 just as 2/6 is. It is not approximate at all. I already proved this, so I think you are either being purposely annoying or just too lazy to actually regard the fact.

2. I don't know if you are being genuinely dumb here, but I have told you that I specifically responded to this, and you just repeat the same thing. The answer would resolve to undefined. Even Wikipedia uses it as an example of fallacious mathematics. Regardless it's completely irrelevant.

You failed to disprove this point, which asserts that Algebraic equations are able to flawed. Meanwhile, your ENTIRE ARGUMENT is based off of Algebraic equations. And also, 0.3333 is the CLOSEST POSSIBLE APPROXIMATE to 1/3, and is likely to be rounded off by 0 at the end of infinity.
0 x 1 = 0
0 x 2 = 0
Therefore,
0 x 1 = 0 x 2
And
(0 x 1) / 0 = (0 x 2) / 0
Which simplifies to
0/0 x 1 = 0/0 x 2
And then
1 = 2
Math is weird, yo.

A quick thing about grading debates:
For arguments it doesn't matter if you win by an inch or a mile, but for every other category it should be a significant lead if points are to be assigned. Not one motspelled word, not one damned curse word, not one bit of bad, punctuation.

Are you a little off because I responded directly to that in my round 3, debunking it easily.

CON's spelling, grammar, and organization was horrible so I believe that goes to me.

Conduct to me because CON used a curse word in round 3.

Arguments to me because CON did not refute any of my arguments and I refuted all of theirs. Both mathematical proofs were still upheld by the end of the debate

I think it may be more of the very last thing you wrote

Excuse me?! Conduct?! Both sides were equally respectful to one another. That is a tie.

I will let Spelling and Grammar slide since CON made a few structure mistakes.

As for arguments, you never responded to CON's claim that 1 = 2, which used the same logic that you did. So, this could go either way.

The level of confidence you emitted with that post is unjustified since you both have an equally strong position.

Or I'm an idiot IDK

So my predictions are as follows:

I think I should win the spelling/grammar point pretty soundly by any standard. I likely won conduct as well, but I am sure that arguments should be going my way. I hope someone is able to vote and I'll let you do your thing.

I did that with 9.999... vs 10 actually

I do, somewhat, make that argument, in Round 2 and more so in Round 3, though not exactly the way you put it.

I feel like every time we have this debate nobody brings up how 0.99..., no matter how many 9's come after the decimal, multiplied by 9 will never equal 9. It will always equal 8 with a certain amount of 9's after the decimal ending with a 1. Like, we're proving the assumption of 0.99... = 1 by using the assumption 8.99...1 =9

"multiplying bothnsides"

Typo that obviously means "multiplying both sides"

Sorry for a few typos, I wrote and edited this on Word, and there seemed to have been some issues transferring it over on here. Didn't double check for them after pasting.

I'll tell you what, I may have some time down the line to debate you if you want.

If we were to debate, I believe I would have a somewhat easier fairing against you. For this person I don't know what to expect, for you, it would not even be close.

Regardless, they are fairly sold arguments.
I don't think simplicity implies weakness.

Much weaker argument than I expected, now wishing I had accepted.

Firstly, because often voters seem to struggle to comprehend my arguments and leave it tied or even erroneously vote against me once (that debate wasn't linked to).

Secondly, I laid out the criteria for me to accept it in previous comments and until literally yesterday, Novice had blocked me which stops me being able to accept his/her/their debates.

If you're so well versed at this topic, why not accept it?

https://www.debateart.com/debates/146-0-999-repeating-equals-1
https://www.debateart.com/debates/1620-0-999-1
https://www.debateart.com/debates/2119-0-999-recurring-is-not-equal-to-1

Is the BOP on PRO to prove that 0.99999999999 has a way of becoming the figure 1 by itself or is there some tricks I'm not seeing?

Increase time to 2 days

I disagree to Ragnar's request.

Increase to 7k

I suggest a low character limit, to make it easier on potential voters.

I have come up with the proper way to counter what Pro will do.

Please see here:

https://www.debateart.com/debates/146-0-999-repeating-equals-1
https://www.debateart.com/debates/1620-0-999-1
https://www.debateart.com/debates/2119-0-999-recurring-is-not-equal-to-1