Instigator / Pro
7
1597
rating
22
debates
65.91%
won
Topic
#3394
0.999 repeating equals 1
Status
Finished
The debate is finished. The distribution of the voting points and the winner are presented below.
Winner & statistics
After 1 vote and with 3 points ahead, the winner is...
Novice
Parameters
- Publication date
- Last updated date
- Type
- Standard
- Number of rounds
- 3
- Time for argument
- One day
- Max argument characters
- 3,000
- Voting period
- Two weeks
- Point system
- Multiple criterions
- Voting system
- Open
Contender / Con
4
1458
rating
7
debates
21.43%
won
Description
No information
Round 1
RESOLVED: 0.999 repeating equals 1
FRAMEWORK
- equal: "In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object."
- Denoted with "=" sign.
- 0.999 repeating: 0.999… represents a sequence of terminating decimals where each number in the sequence is a string of 9's after the decimal point. The first number in the sequence is 0.9, the second number is 0.99, the third number is 0.999, the fourth number is 0.9999, and so on.
C1.
NOTE: "..." indicates repeating.
- 1 ÷ 3 = 0.333... in decimal form.
- 1 ÷ 3 = 1/3 in fraction form.
- Applying this 1/3 * 3 = 1
- Therefore; 0.333...* 3 should also be equal to 1
- Having established this, 3 * 0.333... = 0.999...
- Therefore, 0.999 must be equal to one.
C2.
- We can further illustrate this quite easily with this proof:
- If x = 0.999...
- Then 10x = 9.999...
- 10x - x = 9x
- 9.999... - 0.999... = 9.000...
- so 9x = 9.000...
- When we solve this equation, x = 1.
- Therefore 0.999... = 1.
SOURCES
A few thoughts and counterthoughts to begin with, but, asan introduction:
The opponent’s own sources disprovetheir own arguments, and one sources seems like a poor authority onthe subject.
The opponent’s own sources disprovetheir own arguments, and one sources seems like a poor authority onthe subject.
Business Insider is not a mathematics journal, forum oreducational resource; the author, Andy Kiersz, has given no indication if they've been awarded degrees, or what they are; and their understanding of congruence and mathematical equality contradict Wikipedia’s.
However, given the pro side has restrictedthe character count to a tenth of their other debates, I have to be brief, then expand in later rounds. This means I can only provide a skeleton of a proper argument, due to the opponent's restrictions, and hope the opponent can providebetter sources and proofs, while also disproving universallyaccepted mathematical definitions and concepts, while also providing betterarguments than my own.
First, the Business Insider source and the definition of MathematicalEquality.
1)Their definition of convergence is applied wrong in theirargument. Convergence does not imply equality.
2)Within their own article, the author contradictsthemselves in their closing lines.
"..non-terminatingdecimal expansion actually represents — a sequence of terminatingdecimals that gets arbitrarily close to some number."
Then, in another line:
“all getting really close to 1”
A does not equal ~A.
Definitions of Mathematical Equality:
1)Theopponent’s given definition of equality neither satisfy their implicitdefinition of equality (the definition required to satisfy their argument withtheir mathematical proofs)
2)Nor does itrepresent the full scope or definition of what is meant or understood bymathematical equality.
The incorrectly apply their own definition, and they don’tunderstand the full definition of mathematical equality.
So, to address their proofs.
1/3 does not exactly equal .333…
1/3 is understood to represent a more hypothetical value which is represented in decimal form by the approximate value of .333…
Where theopponent states, “.333…*3 should also be equal to 1 …. Therefore, .999 must beequal to one,”
“The binary relation ‘is approximately equal’ (denoted bythe symbol [~]) between real numbers or other things, even if more preciselydefined, is not transitive (since many small differences can add up tosomething big).” - Wikipedia
This definition of approximate equality--the formof mathematical equality one would use when discussing congruence--becomesespecially true using multiples of x = .999…
1/3 does not exactly equal .333…
1/3 is understood to represent a more hypothetical value which is represented in decimal form by the approximate value of .333…
Where theopponent states, “.333…*3 should also be equal to 1 …. Therefore, .999 must beequal to one,”
“The binary relation ‘is approximately equal’ (denoted bythe symbol [~]) between real numbers or other things, even if more preciselydefined, is not transitive (since many small differences can add up tosomething big).” - Wikipedia
This definition of approximate equality--the formof mathematical equality one would use when discussing congruence--becomesespecially true using multiples of x = .999…
For every multiple of x, the approximate equality become greater and greater.
In addition:
10x – x does equal 9x, but 9x does not equal 9.000…
So there isa flaw in the math presented here.
In addition to expanding on these, I would also like to discuss operations and functions inmathematics necessitated by approximate values, but, with limited space, this is what I have. The opponent now has a vast gulf of discrepancies and 3000 characters.
In addition to expanding on these, I would also like to discuss operations and functions inmathematics necessitated by approximate values, but, with limited space, this is what I have. The opponent now has a vast gulf of discrepancies and 3000 characters.
Round 2
FRAMEWORK
- Everything CON says about the Business Insider source is irrelevant. It was only used in the framework for the "definition"/explanation of .999 repeating so unless CON disagrees with what .999 repeating means, there is nothing to address.
- CON accepts the definition of equality and therefore our framework is agreed upon.
C1 REBUTTALS
- My C1 can be restated in the following syllogism. As you will see CON fails to rebut any of the premises
p1) .333... = 1/3
p2) 1/3 * 3 = 1
p3) .333... * 3 = .999...
c) Therefore .999... = 1
CON argues that I "incorrectly apply [my] own definition," and that [I] "don’t understand the full definition of mathematical equality"
- I don't know how CON got this but looking at their arguments they all ultimately fail to refute anything I said in round one.
CON first says that "1/3 does not exactly equal .333…"
- Totally false 1/3 is exactly equal to 0.333...
- We can use any basic mathematical proof to demonstrate this
- Let's say 0.333... is equal to x
- x = 0.333...
- Therefore 10x = 3.333... (multiplying both sides by 10)
- Therefore 9x = 3 (subtracting x from both sides)
- Therefore x = 3/9
- Therefore x = 1/3
- CON in your response please tell me which one of these steps you disagree with.
"1/3 is understood to represent a more hypothetical value which is represented in decimal form by the approximate value of .333…"
- Source needed?
- Also, the value isn't approximate to 1/3. That would imply it was rounded but as I have just shown, .333... is exactly equal to 1/3.
CON says "This definition of approximate equality--the form of mathematical equality one would use when discussing congruence--becomes especially true using multiples of x = .999…"
- CON's entire case can be summarized on the pillar that .999 repeating is approximately equal or rounded to 1
- This is not the case because I did not use rounding in any of the formulae used to prove that .999 repeating is equal to one. The argument is therefore moot.
- I have proven that .333... = 1/3 exactly and CON drops all other steps of my equations, so they have not refuted my C1.
- Frankly, anything CON posted related to approximate equality is irrelevant
C2 REBUTTALS
CON says "In addition: 10x – x does equal 9x, but 9x does not equal 9.000…"
- But in denying the truth of basic math, CON does not say how or why 9x does not equal 9.000... in my equation, nor does CON state specifically what is wrong with the step.
- I can even restate the equation and justify each step
- If x = 0.999..
- 10x - x = 9x (multiplying bothnsides by 10 and 10 - 1 = 9)
- 9.999... - 0.999... = 9.000... (subtracting .999... from 9.999... produces an infinite string of 0s = 0)
- Therefore 9x = 9.000...
- So we have the equation here. Let's see how CON will deny or insist that 9x does not equal 9.000... in the equation
- As of now, CON has failed to disprove any of my arguments
Back to CON and vote PRO
To reiterate a few things I said.
Business Insider is not an academic or scholastic source on mathematical theory. There are contradictions to what my opponent said, as well as within the Business Insider article itself, and my opponent’s other source, the Wikipedia article, even contradicts what the opponent says on mathematical equality.
The opponent quoted one line from the Wikipedia article about mathematical equality, and seems not to have read anything on congruence and approximate values.
.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.
As far as the steps you take for your proof, you found (you didn’t, someone on Business Insider did) one of the many minor absurdities of mathematics, and you’re abusing the fact that we simplify repeating decimals when converting them into fractions.
The opponent has clearly not read the Wikipedia article still, or else they would understand what an approximate value is. Thus, they have also proven they still incorrectly apply their own definitions, and that they still don’t have a full understanding of mathematical equality.
The next part with x = .999… further proves this. I didn’t say anything about rounding. They still obviously don’t understand what approximate equality is.
An approximate equality is something which almost equals something, but doesn’t quite equal something. Because of this, in mathematics, there’s an idea of errors in approximate values, because you are getting impossibly closer to a hypothetical value (one third being hypothetical because you can never divide a single, real-world object into perfect thirds, only approximate thirds), and a compounding of errors if you were to add approximate values together.
In short, .333 will never quite equal 1/3, and .999… is even further from 1 than .333… is from 1/3
As far as C2, 9 * .999… = 8.999…, and we already went over approximate values, so I don’t need to explain this all over again.
Here’s a source on Xeno’s paradox.
It’s another example of an absurdity/paradox in math. There’s a number of them.
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.
Round 3
RC1
- CON, unfortunately, continues to argue that 0..333...is not equal to 1/3.
- Last round I illustrated a mathematical proof showing they are exactly equal
- CON is unable to show how the math is flawed or wrong.
CON says In my proof I am "abusing the fact that we simplify repeating decimals when converting them into fractions"
- I did not simplify anything im my proof. If you believe I did, show the specific step.
"The next part with x = .999… further proves this. I didn’t say anything about rounding. They still obviously don’t understand what approximate equality is."
- I am not saying approximate equality in of itself means rounding.
- I'm saying when a quantity is deemed approximately equal it must be rounded up to the quantity of approximation in order to be stated as equal to the given quantity.
- 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.
- CON is disagreeing with a fact here.
RC2
"As far as C2, 9 * .999… = 8.999…, and we already went over approximate values, so I don’t need to explain this all over again."
- CON just says this without showing anything as to how they got the answer? Regardless, the answer is incorrect.
- 9 * .999 = 9.000... (repeating into an infinite string of 0s).
- CON is still unable to pinpoint any step in the mathematics that is flawed, illogical, or faulty. Remember this was my C2 proof.:
- x = 0.999...
- 10x = 9.999... (multiplys both sides by 10)
- 10x - x = 9x (subtracts x from left side)
- 9.999... - 0.999... = 9.000... (subtracts x from right side 9)
- 9x = 9.000... (infinite string of 0s = 0)
- x = 1
- Thereofre 0.999... = 1.
MATH PARADOX REBUTTAL
- Both paradoxes CON brings up are completely irrelevant, but I will address the one part because CON's own source refutes their argument. Let's see what it says about the 1=2 "paradox."
- "The fallacy here is the assumption that dividing 0 by 0 is a legitimate operation with the same properties as dividing by any other number. However, it is possible to disguise a division by zero in an algebraic argument,[3] leading to invalid proofs that, for instance, 1 = 2"
- 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).
- CON paints this as a form of inconsistency or gap in mathematics, however, the math is just incorrect. CON's own source literally uses it as an example of fallacious and invalid math.
- My main argument is simple
p1) .333... = 1/3
p2) 1/3 * 3 = 1
p3) .333... * 3 = .999...
c) Therefore .999... = 1
- CON has failed to disporve any of the premises
- Therefore .999... = 1
RC1:
-I'm arguing a truism
-You didn't
-Opponent should why 1 doesn't equal 2
Asking about where you simplified the number is like asking, “Show me in the cooking instructions where it says I should wash my hands.” Cooking instructions usually don't have that step.
It's not about rounding. An approximately equal value is almost equal to something, so we say, “It’s basically equal, for the sake of simplicity, since we don't want a debate on infinity every time we try to divide shit," but they’re not actually equal.
-
9 * .9 = 8.1
9 * .99 = 8.91
9 * .999 = 8.991
Etc.
-
Let’s say I want to find three equally-sized numbers that, when added together, equal ten.
3+3+3=9. Nope.
4+4+4=12. Nope.
3.3+3.3+3.3=9.9. Nope.
3.4+3.4+3.4=10.2. Nope.
I continue doing this for 3.33 & 3.34, 3.333 & 3.334, and so on, until I find the three numbers I can add together to equal ten.
And I get an infinite series of "Nooope".
I never will find three equal numbers that add up to 10 [or 1], however, because I will always have to add an infinitely smaller 3 at the end of the decimal.
There is no A that can satisfy 1 / 3 = A, because there is no A that can satisfy A+A+A = 1.
It’s not about rounding.
It’s that there are no three equal numbers numbers you can add together to get 1, so we just say, "1/3 = .333...".
-
As far as the 0’s.
It’s a fallacy because they simply decided to call it a fallacy because they don’t know what to do with 0’s--not because there’s some inherent attribute a zero has that makes it a fallacy, or some other logical inconsistency to the otherwise infallible and satisfactory operation. They decided it was a fallacy, because they don’t know what happens when you decide by zero.
And that was the whole point of using that in this argument.
I used that as an example of why, sometimes, mathematicians make decisions on weird, fringe cases, such as 1=2 when you divide by 0, or 1=.999,
To reiterate, math is weird.
Finally, if you read the page on Zeno’s Paradox and understood it as well as you understood the part about 0’s, then I’m sure you have a solid grasp on calculus now. So, you ought to understand what a limit and an asymptote is. The easiest one is the inverse function, f(x) = 1/x or y = 1 / x.
So, 1/x = y
1 / 0 = error
1/1 = 1
1/10 = .1
1/100 = .01
1/1000 = .001
1/10000 = .0001
1/100000 = .00001
As X gets bigger, Y gets smaller.
As X gets closer to infinity, Y gets closer to zero.
However, Y will never =0. Y will only approach 0.
Similarly, .333... approaches 1/3, but isn't actually 1/3; and .999... approaches 1, but isn't actually 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