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This Debate Needs Redress

Grape
Posts: 989
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1/24/2011 7:20:46 PM
Posted: 5 years ago
http://www.debate.org...

Only four out of fifteen people who voted on this debate reported that they agreed with the mathematically true proposition that 0.(9) is equal to 1.

Pro offered a correct algebraic proof of the statement and correctly pointed out numerous problems in Con's response, which was complete gibberish that has no mathematical relevance. He argues things like, ".999... is not a whole number, it is infinite."

Con is winning this debate because the people who voted on it do not understand the issue at all and are voting based on their prior beliefs. They are either not reading the debate or not understanding it. In my opinion, this severely reduces the credibility of the site.

I would be against an abusive debate like "2+2=4." However, I grant an exception to this topic because of its educational value. Nonetheless, the current situation is effectively equivalent to Pro losing the "2+2=4" debate because Con argued, "No, 2+2 and 4 are actually slightly different because that's how I feel." When this sort of thing happens on the site, one has to seriously question how seriously the debates are being taken.

It might be inappropriate to judge a debate in this way and say the outcome is wrong, but in this case it simply is. There is absolutely no doubt that Pro's math was correct and that people voted against him because they were mistaken.
Ore_Ele
Posts: 25,980
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1/24/2011 9:15:40 PM
Posted: 5 years ago
At 1/24/2011 7:20:46 PM, Grape wrote:
http://www.debate.org...

Only four out of fifteen people who voted on this debate reported that they agreed with the mathematically true proposition that 0.(9) is equal to 1.

Pro offered a correct algebraic proof of the statement and correctly pointed out numerous problems in Con's response, which was complete gibberish that has no mathematical relevance. He argues things like, ".999... is not a whole number, it is infinite."

Con is winning this debate because the people who voted on it do not understand the issue at all and are voting based on their prior beliefs. They are either not reading the debate or not understanding it. In my opinion, this severely reduces the credibility of the site.

I would be against an abusive debate like "2+2=4." However, I grant an exception to this topic because of its educational value. Nonetheless, the current situation is effectively equivalent to Pro losing the "2+2=4" debate because Con argued, "No, 2+2 and 4 are actually slightly different because that's how I feel." When this sort of thing happens on the site, one has to seriously question how seriously the debates are being taken.

It might be inappropriate to judge a debate in this way and say the outcome is wrong, but in this case it simply is. There is absolutely no doubt that Pro's math was correct and that people voted against him because they were mistaken.

I will challenge you to the same debate, same resolution. I take CON.
"Wanting Red Rhino Pill to have gender"
Grape
Posts: 989
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1/24/2011 9:53:11 PM
Posted: 5 years ago
At 1/24/2011 9:15:40 PM, OreEle wrote:

I will challenge you to the same debate, same resolution. I take CON.

Read my comment in the debate and decide if you are still up for it. I am not going to allow a number system that contains infinitesimals and you aren't going to allow one that doesn't, so I don't see how this debate is going to happen.

In the actual debate, no reference was made to number systems at all and Pro's rules in Round One strongly implied that he assumed they were only using real numbers. I doubt either person in the debate (or indeed anyone who voted for Con) took into consideration extensions of the real numbers.
Ore_Ele
Posts: 25,980
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1/24/2011 11:59:23 PM
Posted: 5 years ago
At 1/24/2011 9:53:11 PM, Grape wrote:
At 1/24/2011 9:15:40 PM, OreEle wrote:

I will challenge you to the same debate, same resolution. I take CON.

Read my comment in the debate and decide if you are still up for it. I am not going to allow a number system that contains infinitesimals and you aren't going to allow one that doesn't, so I don't see how this debate is going to happen.

In the actual debate, no reference was made to number systems at all and Pro's rules in Round One strongly implied that he assumed they were only using real numbers. I doubt either person in the debate (or indeed anyone who voted for Con) took into consideration extensions of the real numbers.

Yes, I would be arguing that limit as x-> n for f(x) = A is not the same as f(n) = A

I would be arguing that .1111111.... =/= 1/9, but that the limit of it equals 1/9.

It is differing between limits and "equals"
"Wanting Red Rhino Pill to have gender"
Ragnar_Rahl
Posts: 19,297
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1/25/2011 12:43:36 AM
Posted: 5 years ago
0.9999... *10 = 9.999... (recurring) (B*10)

A "proof" consists not only of its conclusions, but also its premises. What is the proof of .9... x 10 equalling 9.9.... x 10?

(Don't tell me that multiplication is just moving the decimal, that's a useful pedagogical tool when teaching how to deal with finitely many digits but it is not an argument.)

I remember this coming up on the site before and I don't remember whether I was convinced or not. I think if I was it was by some other proof.
It came to be at its height. It was commanded to command. It was a capital before its first stone was laid. It was a monument to the spirit of man.
Ore_Ele
Posts: 25,980
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1/25/2011 12:45:41 AM
Posted: 5 years ago
At 1/25/2011 12:43:36 AM, Ragnar_Rahl wrote:
0.9999... *10 = 9.999... (recurring) (B*10)

A "proof" consists not only of its conclusions, but also its premises. What is the proof of .9... x 10 equalling 9.9.... x 10?

(Don't tell me that multiplication is just moving the decimal, that's a useful pedagogical tool when teaching how to deal with finitely many digits but it is not an argument.)

I remember this coming up on the site before and I don't remember whether I was convinced or not. I think if I was it was by some other proof.

It was done by a different proof at that time, a .111111111 = 1/9 times both sides by 9 to get .9999999999999 = 9/9
"Wanting Red Rhino Pill to have gender"
Ragnar_Rahl
Posts: 19,297
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1/25/2011 1:06:25 AM
Posted: 5 years ago
At 1/25/2011 12:45:41 AM, OreEle wrote:
At 1/25/2011 12:43:36 AM, Ragnar_Rahl wrote:
0.9999... *10 = 9.999... (recurring) (B*10)

A "proof" consists not only of its conclusions, but also its premises. What is the proof of .9... x 10 equalling 9.9.... x 10?

(Don't tell me that multiplication is just moving the decimal, that's a useful pedagogical tool when teaching how to deal with finitely many digits but it is not an argument.)

I remember this coming up on the site before and I don't remember whether I was convinced or not. I think if I was it was by some other proof.

It was done by a different proof at that time, a .111111111 = 1/9 times both sides by 9 to get .9999999999999 = 9/9

That's assuming the conclusion. No one who doubts that .9999.... =1 does not also doubt that .111.... = 1/9. if they do they'd have to be really stupidly inconsistent, it's the same basic claim with different dressing.
It came to be at its height. It was commanded to command. It was a capital before its first stone was laid. It was a monument to the spirit of man.
Zazzman
Posts: 5
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1/28/2011 7:23:35 AM
Posted: 5 years ago
I'm a math major. I understand that pro is correct.

However, I cannot follow how he laid out his argument. And given how the premise of the debate was to call into question a well-known mathematical idea...

Just because Pro is right, doesn't mean he got there by doing it right. The math in Pro's initial post is so jumbled that I cannot follow it, even though I know exactly what he's trying to do. His second post was closer... but still not exactly what I'd consider absolutely correct.

Right now, I value holding Pro to a higher standard, as one math literate person to another, over punishing Con for the minute errors he can look up.

This smells like Pro just looked up something he could easily prove, just to earn points. In the way he either fudged, mis-copied, or poorly-formatted the original, I see support (but not proof) of starting a debate just to win by mimicking a completed proof.

Especially the way his profile claims to be a gifted High School student, this sort of dishonesty - whether we include using a cheat-sheet in this charge or not - MUST be discouraged.

On that grounds and because of my personal interpretation of what I saw, the only votes of mine which went to Pro are those that I agree with him going in and coming out. The others went to Con.
Ore_Ele
Posts: 25,980
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1/28/2011 12:43:25 PM
Posted: 5 years ago
At 1/28/2011 7:23:35 AM, Zazzman wrote:
I'm a math major. I understand that pro is correct.

However, I cannot follow how he laid out his argument. And given how the premise of the debate was to call into question a well-known mathematical idea...

Just because Pro is right, doesn't mean he got there by doing it right. The math in Pro's initial post is so jumbled that I cannot follow it, even though I know exactly what he's trying to do. His second post was closer... but still not exactly what I'd consider absolutely correct.

Right now, I value holding Pro to a higher standard, as one math literate person to another, over punishing Con for the minute errors he can look up.

This smells like Pro just looked up something he could easily prove, just to earn points. In the way he either fudged, mis-copied, or poorly-formatted the original, I see support (but not proof) of starting a debate just to win by mimicking a completed proof.

Especially the way his profile claims to be a gifted High School student, this sort of dishonesty - whether we include using a cheat-sheet in this charge or not - MUST be discouraged.

On that grounds and because of my personal interpretation of what I saw, the only votes of mine which went to Pro are those that I agree with him going in and coming out. The others went to Con.

I thought it was rather easy to follow. It is a different proof then what I normally see, but it wasn't hard to adjust to it.
"Wanting Red Rhino Pill to have gender"
Grape
Posts: 989
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1/28/2011 1:35:47 PM
Posted: 5 years ago
At 1/28/2011 7:23:35 AM, Zazzman wrote:
I'm a math major. I understand that pro is correct.

However, I cannot follow how he laid out his argument. And given how the premise of the debate was to call into question a well-known mathematical idea...

Just because Pro is right, doesn't mean he got there by doing it right. The math in Pro's initial post is so jumbled that I cannot follow it, even though I know exactly what he's trying to do. His second post was closer... but still not exactly what I'd consider absolutely correct.

Right now, I value holding Pro to a higher standard, as one math literate person to another, over punishing Con for the minute errors he can look up.

This smells like Pro just looked up something he could easily prove, just to earn points. In the way he either fudged, mis-copied, or poorly-formatted the original, I see support (but not proof) of starting a debate just to win by mimicking a completed proof.

Especially the way his profile claims to be a gifted High School student, this sort of dishonesty - whether we include using a cheat-sheet in this charge or not - MUST be discouraged.

On that grounds and because of my personal interpretation of what I saw, the only votes of mine which went to Pro are those that I agree with him going in and coming out. The others went to Con.

I still think Pro made better arguments, but you make a very legitimate point. However, the main thing I have a problem with is that many people who voted against him disagreed with him after the debate. This makes me think that he was losing because people on the site were ignorant of the topic, which as I said would be a very make problem as far as the integrity of our voting system goes.
Logic_on_rails
Posts: 2,445
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1/28/2011 3:39:41 PM
Posted: 5 years ago
Zazzman, I didn't just make the debate to have an easy win, as much as it could seem that way. By 'gifted' I would take a successful entry score of a government sanctioned test determining people of a 'gifted' nature to be reasonable proof, although in no way final proof. I made the debate for a few reasons, to test my formatting skills, encounter potential new mathematical concepts (if you've seen my profile you know that I'm only just going into year 9) , test for semantics and see how people voted.

I've been particularly interested in how people have voted, like yourself. You gave 7 points to Con. No RFD, and no possible explanation. No side used any sources, certainly my opponent did not have better spelling or grammar and as for conduct how did I lose for conduct in the debate, where if anything my opponent was unkind to reading for voters. Finally, even if you believe my opponent made better arguments, that should only be a 3 point vote, although his arguments were unclear to say the least, and I believe you agree here. So again why the 7 point vote?

I agree this was a test run and next I'll do something far more complex, but as Grape noted, people were voting very strangely and unjustifiably (7 pointers) .
"Tis not in mortals to command success
But we"ll do more, Sempronius, we"ll deserve it
Zazzman
Posts: 5
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1/28/2011 5:58:42 PM
Posted: 5 years ago
At 1/28/2011 3:39:41 PM, Logic_on_rails wrote:
Zazzman, I didn't just make the debate to have an easy win, as much as it could seem that way. By 'gifted' I would take a successful entry score of a government sanctioned test determining people of a 'gifted' nature to be reasonable proof, although in no way final proof. I made the debate for a few reasons, to test my formatting skills, encounter potential new mathematical concepts (if you've seen my profile you know that I'm only just going into year 9) , test for semantics and see how people voted.

I've been particularly interested in how people have voted, like yourself. You gave 7 points to Con. No RFD, and no possible explanation. No side used any sources, certainly my opponent did not have better spelling or grammar and as for conduct how did I lose for conduct in the debate, where if anything my opponent was unkind to reading for voters. Finally, even if you believe my opponent made better arguments, that should only be a 3 point vote, although his arguments were unclear to say the least, and I believe you agree here. So again why the 7 point vote?

I agree this was a test run and next I'll do something far more complex, but as Grape noted, people were voting very strangely and unjustifiably (7 pointers) .

Yes, "gifted" is generally used in a very specific way regarding test taking skills. However, to say that some test would be the only evidence of such would be foolish. You attend such a selective school, and "dominate even within selective," it would be rash to discard such evidence.

On how he cited better evidence than you - I'm simply holding you to a higher standard. He could at least claim that his position came from his understanding of calculus. Those points where he is in error, he can look up.

I could complain about how you cited no existing theorems nor proved them as your basis, as another user did. Citing or assuming theorems may be a cheap shot, but since the conceptualization of transfinite numbers by Cantor, you quite literally have to prove or cite that 1 + 1 = 2. This would be over the top.

You formatted the math in the first post in such a way which I found hard to follow. Adding parenthetical comments as if your math as if it were a sentence made this formatting awkward, in the very least. Instead, I suggest you start from your premise, and work every single step out. I would personally accept "computation" as your backing for:
10 * .999... = 9.999...
because if we can't trust simple computation when lacking the training to prove it, what can we trust? Now we have to prove that 1 + 1 = 2 all over again.

A = 1 by definition
10 * A = 10 * 1 by substitution
10A - A = 10 - 1 " "
. 9A = 9
(really, not necessary!)

B = .999... by definition
10 * B = .999... *10
by substitution, and the commutative property of multiplication.
10 * B = 9.999... by computation
(I'll take it for now, but if Con disputes, we gotta prove it - but it
is visually easy enough to see without a formal proof)
10B - B = 9.999... - .999....
9B = 9

Eh, why not just go for it here? It's clearer for readers.
9B * 1/9 = 9 * 1/9
B * 9/9 = 9/9 (by commutative and inverse properties of multiplication)
B = 1
.999... = 1
QED

But instead, you used the bijectivity of the relation 10x - x => 9x over Real numbers. Since this relation puts out that both 9A and 9B are both equal to 9, that must mean that A = B.

What's the difference? I cited a few properties to hold the readers's hand, and stuck to more basic logic.

The biggest difference I went through the proof in a *linear* way. This way, we don't have a jump around to piece together logic unnecessarily. After a long night, even I can stumble over putting together those pieces.