1 and .999 repeating are the same quantity. Exactly equal.
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After 2 votes and with 6 points ahead, the winner is...
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I argue that .999r IS NOT approaching the number 1. Does NOT estimate or round to the number 1. But is in fact the same as the number 1.
By round or estimate to the number one I do not mean the syntactic changing of one number to another. And that any rounding that may occur is no different than rounding 2.000 to 2. They are the same number.interchangeable.
When rounding a number, you first need to ask: what are you rounding it to? Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, and so on.Consider the number 4,827.4,827 rounded to the nearest ten is 4,8304,827 rounded to the nearest hundred is 4,8004,827 rounded to the nearest thousand is 5,000All the numbers to the right of the place you are rounding to become zeros. Here are some more examples:34 rounded to the nearest ten is 306,809 rounded to the nearest hundred is 6,8001,951 rounded to the nearest thousand is 2,000
Pro sets up a rather clear equation on which to base his comparison, explaining that by turning each of the fractions he's presented into a decimal, you can find that adding them together leads to a number that is not 1, in spite of the fact that adding those two fractions together does result in 1. The difference is infinitesimally small, but it does exist. He's essentially stating that the number 0.000r is equivalent to 0 for the same reason. While I understand Con's responses regarding the need to round in order to get a real number, I don't think that's necessary when you're comparing what is, effectively, an unmeasurable quantity. That's what Pro is doing with his argument, and while I think he could have defended it better, I don't think just railing against the lack of rounding suffices as a reason for me to vote Con. I do think there are ways to challenge this that involve more complex math, but those aren't presented, leaving me with little choice but to vote Pro.
The instigator's position is a truism. There is no serious debate in mathematics as to whether or not 0.999r = 1. The reason people have a difficult time grasping how 0.999r = 1 has to do with difficulty grasping an infinite series. We are accustomed to the finite and the infinite is something that simply isn't part of our everyday experience, and this is where Pro's position is weakest. Pro merely posits that 1/3 = 0.333r and that 2/3 = 0.666r. This is a bare assertion, but is later supported rather weakly. This assertion is attacked by Con with his rounding argument. However, Con's attack fails because Pro correctly pointed out that no rounding was being supposed. Con's other attack with the 2.9999(r)7 also fails because Pro correctly pointed out that this was a change in terms (i.e. off topic, and this is true - The topic is 0.9999(r).
Please focus on the debate resolution.
Kid your rating is the default rating.
You make a good point about the simple fact that PRO doesn't type all of the decimal places out explicitly means that they are (de facto) rounding.
1/3 =/= 0.33333(r) without rounding
2/3 =/= 0.66666(r) without rounding
3/3 =/= 0.99999(r) without rounding
All of your efforts to use rounding as examples are moot because PRO already excluded rounding explicitly.
All you have to prove is that PRO requires rounding in order for their case to be true and since PRO already excluded rounding as an option, they have sabotaged their own case.
I view a debate like a basketball game. If your opponent fails to put the ball in the hoop, that does not mean you win automatically. You actually have to put the ball in the hoop. And in my opinion, the best way to do that is with a syllogistic statement that either proves (PRO) or disproves (CON) the debate resolution.
1/3 + 2/3 = 3/3
3/3 = 1 (you will never ever conclude that 3/3 = 0.9 recurring without the context that Pro is tricking you into taking as valid reasoning).
1/3 when rounded to the nearest thousandth is 0.333
2/3 when rounded to the nearest thousandth is 0.667
So if we do actually round correctly, the answer even with decimals replacing fractions is 0.333 + 0.667 = 1.000 =/= 0.999
What Pro is arguing is that if you never ever rounded the 2/3 to end up with a 7 at the end of it (since you round up 0.6 recurring to end with a 7 no matter what) then you'd never end up with the answer of 1 as opposed to 0,9 recurring as the result of 1/3 + 2/3. This 'I'm so smart' quip made by people who think they are math geniuses fails to admit that if a number is recurring, you never ever could finish writing or delivering the answer in any way at all. What I mean by this is that the millisecond you stop typing '6' and '9' you're betraying yourself as you're rounding the answer and if you round the answer you never ever, ever, ever will get anything but 1.000000 (to whatever decimal point you rounded to).
Now let me give you actual 'I am smart and good at math' sums that make the resolution impossible.
0.9 *3 = 2.7
0.99 *3 = 2.97
So if one is to ever conclude that 3/3 = 0.9 recurring there is at some point a '3' that they are ignoring needs to be added on to the '7' in order to ever make this true.
Therefore if we are ever tricked by the formatting of sum to conclude that 1/3 + 2/3 = 3/3, we must remind the one tricking us to remember the '7' that never can end up being a '10' so as to make this answer true.
3/3=1
0.99999(r) =/= 1
3/3 =/= 0.99999(r)
This is a problem of precision.
Focus on the actual debate resolution and not the supporting arguments.
alright, there's actually something missing in your brain if you think that.
3/3 was the entire argument Pro themselves made and 3/3 is in fact 1 and not .9recurring as proven by me and thus if they are 'exactly equal' this would never be able for me to have proven.
3/3 is not the debate resolution.
What's 3/3? Stop being dumb and smart at the same time.
I see a couple of problems.
Death23's vote would seem to be invalid because their RFD begins with a long explanation of why they agree with PRO prima facie, which I believe constitutes fabrication of a new argument. They also seem to have misunderstood CON by stating CON requires rounding to make their case.
PRO defeats theirself in round 2 with, "...when you add zero to any number, it equals the number itself. So if the difference between 2 numbers is not zero. They are not equal."
CON's best case was in round 2 with, "Your resolution is impossible because: EITHER - We round and get 1 and/or 3. - OR - We don't round and admit that '7' which is missing in that 0.9recurring * 3 so it can never truly be 3 and thus 3/3 can't be 0.9recurring. Checkmate."
This argument of CON unfortunately fails to address the actual debate resolution, namely "1 and .999 repeating are the same quantity. Exactly equal."
PRO's defense in round 2 of, "Therefore, there is no quantity between 1 and .999 repeating. The difference between them is "zero"." is provably false and this is perfectly clear because of the fact that they had to make a point to quarantine their use of the word zero in quotes explicitly because of what they argued also in round 2 was "If we take 1 and subtract .999 repeating we are quick to say the answer is an infinite set of zeros then a 1. ie .00000..infinity..somehow ends in a 1." which is "virtually zero" and obviously NOT actually zero. PRO uses rounding (between virtually zero and zero) when they already explicitly disqualified rounding.
CON makes what I would consider a mistake in round 3 with, "Pro concedes that..." and "Pro further concedes..."
The use of the term "concedes" is loaded and should be reserved. Also, if CON believes that PRO defeated theirself, a quote would be in order.
Why was my argument, while not the same as yours, the 'wrong way' to prove my case?
Your question is off-topic.
You seem to have abandoned the debate resolution.
Well, you seem to be having problems with the more complex aspects of this equality so I was trying to break it down to a simple enough level that you could deal with it. But you don't seem at all interested in figuring out why the resolution is true, and just want to spout of stuff about stuff that doesn't exist.
If you are actually interested in learning why 0.999(r) does equal 1, shoot me a PM. But you have to be prepared to address specific points or answer simple questions, rather than just blanket ignoring them here.
Your question is off-topic.
You seem to have abandoned the debate resolution.
You didn't answer the question.
The only way 0.333333333(r) x 3 = 1 is with rounding. PRO already excluded rounding. Case closed.
True or false:
1/3 x 3 = 1?
0.0000(any number of zeroes)000010000000000000000000(r) is not equal to zero.
What we have is a precision problem.
The only way 0.333333333(r) x 3 = 1 is with rounding. PRO already excluded rounding. Case closed.
"0.0000(r)00001 will always be a quantifiable non-zero difference.
0.0000(any)00001 will always be a quantifiable non-zero difference."
Those are not quantifiable non-zero differences. Those aren't numbers.
Which of the following do you think are wrong?
A) 8/9 = 0.8888(r)
B) 1/9 = 0.1111(r)
C) 8/9 + 1/9 = 9/9 = 1
D) 0.8888(r) + 0.1111(r) = 0.9999(r)
E) 0.8888(r) + 0.1111(r) = 1
You wrote, "Because the difference between 1.0000(r) and 0.9999(r) would be 0.0000(r)00001"
0.0000(r)00001 will always be a quantifiable non-zero difference.
0.0000(any)00001 will always be a quantifiable non-zero difference.
What you are describing with your 9/9 and 3/3 examples is a fundamental problem with the base ten decimal system.
We are forced to round up.
Mhykiel already explicitly denied rounding up.
If we were using a base eight system, the problem would happen with eight instead of nine.
If we were using a base sixty system, the problem would be with fifty nine instead of nine.
This is a fundamental problem of accuracy.
It makes no sense to say that the difference between 9 and 10 is somehow less (or less significant) than the difference between 8 and 9.
Neither "0.0000(inDEfinite)10000000(r)" nor "1.0000(inDEfinite)999999999(r)" are valid numbers.
I've posted several proofs and you're just ignoring them. Which of the following do you think are wrong?
A) 8/9 = 0.8888(r)
B) 1/9 = 0.1111(r)
C) 8/9 + 1/9 = 9/9 = 1
D) 0.8888(r) + 0.1111(r) = 0.9999(r)
E) 0.8888(r) + 0.1111(r) = 1
0.9999 + 0.1111 = 1.1110
0.9999 + 0.0001 = 1.0
0.0001 will always be a quantifiable non-zero difference.
The debate resolution is provably false.
Also, if you add 0.0000(inDEfinite)10000000(r) to 0.9999(inDEfinite)99999999(r) you end up with 1.0000(inDEfinite)999999999(r) which is still not identical to 1.0000(r)
Because the difference between 1.0000(r) and 0.9999(r) would be 0.0000(r)00001 (That is, an infinite number of zeros followed by a 1 - an absurdity) while the difference between 0.9999(r) and 0.8888(r) is simply 0.1111(r).
And this is all consistent:
0.8888(r) is 8/9 in fractional form.
0.1111(r) is 1/9 in fractional form.
8/9 + 1/9 = 9/9 = 1
0.8888(r) + 0.1111(r) = 0.9999(r) = 1.0000(r)
"This equality only applies to numbers ending in point nine repeateing."
By what criteria do you propose that the difference between 1.00000000(r) and 0.9999999999(r) is trivial (AND) the difference between 0.999999999(r) and 0.8888888888888888(r) is non-trivial???????????(r)
x = 0.9999(r)
10x = 9.9999(r)
10x - x = 9.9999(r) - 0.9999(r)
9x = 9
x = 1
I did that except I multiplied it by 3 to accentuate it.
it absolutely follows.
It does not follow that if 0.9999r = 1.0000r then 1.1111r = 1.0000r
The argument isn't that x.yyyy(r) = (x-1).(y+1)(y+1)(y+1)(y+1)(r) but rather that x.9999(r) = (x+1).0000(r). This equality only applies to numbers ending in point nine repeateing.
Your "proof" should be, The resolution "1 and .999 repeating are the same quantity. Exactly equal." is FALSE prima facie.
There is an obvious 0.111111111111(r) difference which is a non-zero numeric value. End. Of. Story.
And why is my disproof insufficient?
I'm not supposed to fabricate arguments when voting.
However, it sounds like Mhykiel needs to support the hypothesis that -
(IFF) 0.99999999999(r) = 1.000000000000(r) (THEN) 1.11111111111111(r) = 1.0000000000000(r) (AND) 0.1111111111111(r) = 0.000000000000000(r) (THEREFORE) 0.11111111111111(r) + 0.99999999999999(r) = 1.111111111111111111(r)
This seems problematic.
For example, (IFF) 0.11111111111111(r) = 0.0000000000000000000(r) (THEN) 0.999999999999999(r) = 0.8888888888888888888(r) (AND) 0.88888888888888888(r) = 0.77777777777777777(r) (THEREFORE) 1.000000000000000(r) = 0.777777777777777777(r)
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>Reported Vote: Ethang5 // Mod action: Removed
>Points Awarded: 5 points for arguments, S/G, and conduct
>Reason for Decision: Pro used precise mathematical terms for his position. That precision was important to his conclusion. Con decided to round, but that wes not what pro was asserting, and he showed why that was incorrect by using other math properties. I think also con rushed to state that pro had conceded.
>Reason for Mod Action: The voter failed to sufficiently explain S/G points. The voter must make it "clear from the vote why a given argument is difficult to read" in order to award these points. The voter failed to sufficiently explain conduct points. In order to award these points, the voter must reference specific instances of poor conduct, explain how these conduct violations were excessive or severe, and compare the two debaters' conduct. Finally, the voter failed to sufficiently explain argument points. The voter must references specific arguments and must weigh those arguments in order to award argument points; neither of these things was done.
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actually it was pro who had to round to make his point true.
You're a rather delusional individual if you think k saying something is a truism and IG original the relevance of the nberultiplied by three has on the topic.
This topic is factually incorrect just so you know. The voter has a delusion that the 97point with 3 was irrelevant but it's directly relevant just as much as the missing 1 in .9r
y = x^x^x^x^x^x^x^x^x^x^(repeating) = 2
x^y = 2
y = 2
x^2 = 2
x = sqrt(2)
;-)
Correction
.333 repeating subtract .333 equals .00033333333 repeating.
If I felt that fact had an ample supply of nay sayers I might argue that as well.
Debate is a means of formal argumentation. It generally requires some room for debate. There really isn't much room when it comes to mathematical facts. Might as well debate that 2+2=4
Isn't debate a means of discerning truthful or factual statements from nonsensical ones?
I think it's surprising the number of people who don't accept debate postulation as truthful.
Are mathematical facts up for debate?