1554

rating

15

debates

73.33%

won

Topic

#1392
# 0.999... = 1

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Finished

All stages have been completed. The voting points distribution and the result are presented below.

With 8 votes and 38 points ahead, the winner is ...

Nemiroff

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- Education
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1294

rating

75

debates

18.0%

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Round 1

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

Nonsense 1 is greater than anything less than one even by a bit

Round 2

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

you are splitting hairs , literally!

Round 3

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

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.

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.

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?

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.

I wish that were always true, especially in online debate channels :p Perhaps if i knew the person better.

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

Well that settles that lol.

This does negate one of my arguments in another debate so thats vexing. Lol

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....

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.

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.

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.

I can take your challenge if you like :D

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

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.

*******************************************************************

>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

******************************************************************

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

*******************************************************************

>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

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:

*******************************************************************

>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.

*******************************************************************

"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...

I have had enough of your bullshit, welcome to the blocklist.

Are you making up definitions?

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

*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.

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