The Instigator
donald.keller
Pro (for)
Losing
2 Points
The Contender
kazmo
Con (against)
Winning
22 Points

Theoretically, It is possible to Divide by Zero

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Post Voting Period
The voting period for this debate has ended.
after 7 votes the winner is...
kazmo
Voting Style: Open Point System: 7 Point
Started: 8/10/2013 Category: Science
Updated: 3 years ago Status: Post Voting Period
Viewed: 5,016 times Debate No: 36556
Debate Rounds (3)
Comments (33)
Votes (7)

 

donald.keller

Pro

In Theory, it is possible to Divide by Zero.

I will take Pro on this, therefore BOP is on me.

R1 is acceptance.
R2 will be the debate.
R3 is the Conclusion Round.

============================================

kazmo

Con

I accept on taking the con side of this debate. In theory, it is not possible to divide by 0.
Debate Round No. 1
donald.keller

Pro

Starting now with the Basics.

==============================================================

The below image helps us understand the basics.


As we can see from it, our Starting Point (Dividend) is 4. From there we have two paths, Negative and Position. Negative Numbers moves backwards, going from 4, to 3, to 2, etc... Postive Numbers move forward, from 4, to 5, to 6, etc...

The problem when reaching Zero is that you can't. Zero is the smallest possible number. Even for numbers in the negative (-1, -2, -3) as those numbers represent a debt, and zero represents the smallest debt.



The reason it's impossible to reach Zero without jumping numbers, is that counting down, you will find yourself counting forever.

This is where Theory comes in. As theory goes, a number can get infinitely smaller. You began your journey counting to Zero...

1... 1/2... 1/3... 1/4... 1/5... ... .... ... 1/10,000,000,000... ... ... ... ... ... ... 1/50,000,000,000,000,000,000,000...

You will count down forever, and unless you jump a Whole Number, you will never reach Zero. This is because a number can always get smaller before hitting Zero.

The reason this doesn't apply to other Whole Numbers the same way is because of Division....

5 / 4 = 1.25
8 / 3 = 2.67

With this, we see that each Whole Number is an attainable amount, while Zero is not.

5 / 0 = ?

This shows us that Zero is can't be reached, because unlike the other Whole Numbers, it's amount is infinitely small. This can be seen in the following numbers...

0.00000000000000000000000000000000000000000000000000000000000000000... ... ... 000000000001

The number above has one trillion zeros in it... It is NOT Zero.

0.00000000000000000000000000000000000000000000000000000000000000000... ... ... 0000000000...

The above number has an infinite amount zeros... There is no 1 or 5 or 6, etc, at the end because there is no end. This is Zero. Or what can be better called Literal Zero.

There is another reason why this logic doesn't apply to the other Whole Numbers. That reason will be seen a little further down.

Because you will have to count down infinitely to reach absolute Zero, it is infintely far from every other number... This leads us into the next part...


The above chart shows us a basic principle of Division...

Every Division has three parts..
(Dividend) / (Divisor) = (Quotient)

The principle is that the smaller the Divisor (seen in red), the larger the Quotient (seen in green.) The Dividend is in the yellow box.
Now the larger the Divisor, the smaller the Quotient.

What this means is that the further back the Divisor, the further up the Quotient, no matter where the Dividend is.



Since, theoretically, Zero is infinitely far back from any number, the Quotient will be equally infinitely far forward. This is because if you Divide something by Zero, following the principle that the smaller the Divisor, the larger the Quotient, and how Zero is infinitely small, the Quotient will be infinitely large... Or Infinty.

Therefore:
5 / 0 = ?

Is actually...

5 / 0 =

This can be calculated as well... As 5 / 0.0000000...01 (with a trillion zeros) will still produce a finite amount, as will 5 / 5.0000000...01 (trillion zeros) but only 1 / 0.00000....00.. (infinte zeros, a.k.a. Literal Zero) will equal Infinity. This is the second reason why the logic does not apply to other Whole Numbers.

This is because, as a Whole Number, Zero can be continously added forever into any number, an infinite number of times. Therefore you can, theoretically, divide a number an infinite amount of times off Zero.

==============================================================

This is only one half to the Theory.

The other half is the Principle seen below...

100 / 50 = 2
100 / 2 = 50.

The Quotient and Divisor can be switched to find each other. Another example...

72 / 12 = 6
72 / 6 = 12

624 / 64 = 9.75
624 / 9.75 = 64

This principle stands in all cases... A triangle effect.

With this, we can see that a number divided by Zero equals infinity by dividing by infinity.



We find that, no matter how far we go, the size of Infinity is so great, that the Dividend will NEVER be large enough to be broken down... And therefore you are left with an infinite stream of zeros....

0.00000000000000000000000000............ ....... .... .... 000000000000000000000... .... 0000000000 (infintely)

And as prior explained, that (and only that) is literally Zero. The result you get is literal Zero.

By the basic Principle prior mentioned, if...

5 / ∞ = 0
Than...
5 / 0 =

And so on....

=========

By both Principles, especially the second one, it is completely possible to Divided by Zero, at least, in theory.

Thank you. Con's turn to argue.
kazmo

Con

Thank you Pros, you have given some of the basics for this debate but I would like to add some more. After this, I will move onto explaining why your proof is incorrect. This topic is hard to debate about because there is a solid answer.
---------------------------------------------------------------------------------------------------------------
There are 5 reasons why any number cannot be divided by 0:
1. Dividing x÷0 = y would mean x*y = 0 which is impossible when given actual values.
2. Vertical slopes are undefined.
3. When Graphing f(x)=1/x, there is no specific value for when x=0, it approaches either -∞ or +∞.
4. Division is repeated subtraction, and it doesn't work with division of zero.
5. If dividing by 0, you would algebraically be able to prove that 1=2, 2=3, 4=5 and so on.


We all know the formula for calculating slopes,


The numerator of the equation is the change in y-values and the denominator is the change in x-values



On this graph, you can see that the change in y-values is just 1. However, when you look at the denominator, you find out that there is no change in x-values. No change whatsoever which yields the denominator being 0. We all know that the slope of a vertical line is undefined and since the numerator is 1 and the denominator is 0, 1÷0 is also undefined.

When you graph f(x)=1/x you you will notice that there is no definite answer when x=0. There is actually an asymptote at x=0. However, in the following images, you will also notice that as you get closer to closer to 0 from left and right, the number goes further and further away from 0 (gets bigger in the positive side and smaller in the negative side).

This arrives at your understanding where it "approaches" +∞. You cannot forget that as x approaches 0, y also approaches -∞ or +. This is going to be a major part of your flaw.

I am going to introduce a special way to do division:
15÷5 = 5+5+5
15÷3= 3+3+3+3+3

Now here comes the error:
15÷0 = 0+0+0+0+0............................
This is impossible to complete because no matter how many 0's you add, you will never reach 15 which is another reason why it is impossible to complete a division by 0.

Lastly, if dividing by 0, you would algebraically be able to prove that 1=2, 2=3, 4=5 and so on. There is a very famous mathematical fallacy in which you are able to prove that 1=2, however there is an invalid proof somewhere in the steps of doing so, making it a fallacy.



As you can see, in the initial observations, the procedure seems legitimate and correct, but I have to call your attention to the first line where a = b and the fourth line where you cancel (a-b) on both sides of the equation. The invalid proof of this fallacy is in line four where you cancel (a-b) on both sides because that is when a division by zero occurs. Remember when I said a=b in the first line? If a = b would (a-b) not just be (a-a)? We all know that (a-a) is equal to zero so that is why 1≠2.
---------------------------------------------------------------------------------------------

Now, to clear up the misconception that you have. Your idea is logical but it is flawed and that is why mathematicians all agree that any number divided by 0 is still undefined.

First off, I would like to bring up a contradiction in your theory. You said that "Zero is can't be reached, because unlike the other Whole Numbers, it's amount is infinitely small." Then, in the second part of your theory, you said that "5÷∞=0", now isn't that a bit contradicting?

You say that as you try to count down "1... 1/2... 1/3... 1/4... 1/5... ... .... ... 1/10,000,000,000... ... ... ... ... ... ... 1/50,000,000,000,000,000,000,000...", it is impossible to completely reach 0. This could also be said with ∞ on the right side of the number line, 1, 10000000, 10000000000000, 1000000000000000000...., with your logic, you can never reach ∞ either so that means you said it yourself that anything divided by zero is impossible to reach infinity, only close to it. The problem here is that you do not arrive at 0 or ∞, you only get closer and closer to them. This is fundamental in the case of limits in calculus, you approach but you don't get to.

Another argument, in the sequence of numbers 1/(1/2), 1/(1/3), 1/(1/4) (notice that it is going down to 0), the sequence turns out to be 2,3,4, ...., ∞ and since ∞ is not a number, it is an idea, there is no value for it which is why we say it's undefined. If you want to assign a value to infinity, sure! Let ∞ = a real number and that 1/0 (5/0) is ∞ just like you said. Then look at a sequence starting from the other side of the number line. 1/(-1/2), 1/(-1/3), 1/(-1/4), ..., and notice again that the denominators -1/2, -1/3, -1/4, ..., are approaching zero. Now, the sequence would be -2,-3,-4,...,-∞. So now we have two infinities, negative or positive infinity? Instead of assigning a fruitless answer, we say that infinity isn't a number, and that 1/0 is undefined.

Please pros, it is your turn to conclude the debate.




Debate Round No. 2
donald.keller

Pro

Thank you Con.

Theoretical: Adj.

1: confined to theory or speculation often in contrast to practical applications
2: existing only in theory(1)
3: of, pertaining to, or consisting in theory; not practical(2)
4: Of, relating to, or based on theory.
5: Restricted to theory; not practical(3)

1) http://tinyurl.com...;
merriam-webster
2) http://tinyurl.com...;
dictionary.reference
3) http://tinyurl.com...;
thefreedictionary

The Resolution is that it's Theoretically possible... In Principle, not in actual Practice.

I need to prove that in theory this would work, not that it actually works.

1. Dividing x÷0 = y would mean x*y = 0 which is impossible when given actual values.

(x / 2 = y)
10 / 2 = 5
But...
(x * y = 2?)
10 * 5 = 50

3. When Graphing f(x)=1/x, there is no specific value for when x=0, it approaches either -∞ or +∞.
Graphing is only the application of a function (see definition 1).

4. Division is repeated subtraction, and it doesn't work with division of zero.
"Now here comes the error:
15÷0 = 0+0+0+0+0..................
This is impossible to complete because no matter how many 0's you add, you will never reach 1..."

You have proven my entire point, completely.
15 / 0 = 0+0+0+0+0.... infinitely. Therefore the answer is infinity... It never ends.

You would keep on adding.
15÷5 = 5+5+5
You add 5 three times, therefore the answer is 3.

15÷3= 3+3+3+3+3
You add 3 five times, therefore the answer is 5.

15÷0 = 0+0+0+0+0....
You add zero infinitely, therefore the answer is infinity.

Since you would keep adding zero forever, you will never reach the end, therefore you can conclude the answer is an infinity.

Thanks for proving my thesis :)

5. If dividing by 0, you would algebraically be able to prove that 1=2, 2=3, 4=5 and so on.
This fallacy is irrelevant to whether or not you can theoretically divide by zero. It only proves that 1 does not equal 2. The concept of 1 equaling 2 has nothing to do with this.

It only shows that dividing by zero does not let 1 = 2 or 2 = 3.

Your idea is logical but it is flawed and that is why mathematicians all agree that any number divided by 0 is still undefined.

If it is logical, than it'd work only in theory... Therefore making it theoretical.

2: existing only in theory(1)
3: of, pertaining to, or consisting in theory; not practical(2)
5: Restricted to theory; not practical(3)

Although your 4th example only further prove my logic by saying that you would add zero an infinite time, therefore the answer is infinity, as my theory claims.

You said that "Zero is can't be reached, because unlike the other Whole Numbers, it's amount is infinitely small."

No, this only proves my theory.

Since Zero is infinitely small, the Quotient will be infinitely large. You're fallaciously misrepresenting the logic.
The smaller the Divisor, the larger the Quotient. If Zero (divisor) is infinitely small, the Quotient is infinitely large (infinity.) Not 'close' to infinitely large, but actually infinitely large.

∞ and since ∞ is not a number, it is an idea, there is no value for it which is why we say it's undefined.

Zero is also, technically, only an idea. But Zero and Infinity is a number... listen.
Infinity is the concept of a never ending number. Since dividing by zero, as you have said (argument 4) leaves us adding a never ending amount of zeros, the answer is literally infinity.

=======================

With your 4th Argument, and final argument, you've only further proven my point.

Zero is infinitely (not near infinitely, but actually infinitely) small. Infinite is infinitely (not near infinitely, but actually infinitely) large. The smaller the Divisor, the large the Quotient. If the Divisor is infinitely small (zero) than the Quotient is infinitely large (infinity).

Infinity is the concept of a never ending number...
The Con himself has admitted that dividing by Zero would leave us adding Zero continuously, never ending...
If the Quotient is the number of times you can add the Divisor into the Dividend, and (as he actually said) you would be adding Zero into the Dividend an infinite times, the Quotient is Infinity.

100 / 25 = 25 + 25 + 25 + 25 (4 times)
The Quotient is 4.

100 / 10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 (10 times)
The Quotient is 10.

100 / 50 = 50 + 50 (2 times)
The Quotient is 2.

100 / 0 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0...... (infinite times)
The Quotient is Infinity.

You, yourself, have admitted this when you said...
"...no matter how many 0's you add, you will never reach 15"
So you will continuously add forever (infinitely,) and based on you 'special way to do division,' this means the answer is Infinity, as my theory said.

As the Resolution goes, the concept of Dividing by Zero is only theoretical. While it doesn't follow every principle (the principle of reverse math) it does follow nearly every principle of basic division.

1: confined to theory or speculation often in contrast to practical applications

The Con never rebutted my R2 arguments, so they still stand.

I have proven, that while not practical, it works in theory.
kazmo

Con

Firstly, in order to correct your understandings:
Dividing x/0 = y would mean x*y = 0 which is impossible when given actual values.
(x / 2 = y)
10 / 2 = 5
But...
(x * y = 2?)
10 * 5 = 50
I did not say that the denominator was 2, I said if the denominator was 0,
If we continue with the correct denominator:

5/0=;
*0 = 5

See? In this case, there is no possible way for the previous equation to be true. Anything, even multiplied with 0 is still 0. This is not a valid equation.

Thirdly, Division is repeated subtraction, and it doesn't work with division of zero. Actually, I have not proven your point. 15/0=0+0+0+0+0+0+0+0+0....,
"Since you would keep adding zero forever, you will never reach the end, therefore you can conclude the answer is an infinity". The problem with your statement is that even if you add zero forever, you will never reach the end because there is no way to end it. There will be no change, it does not approach anything. You have to understand that 0 is nothing, adding nothing to nothing is still nothing. I personally have never used the term "never ending" when referring to 15"0=0+0+0+0+0+0+0+0+0...., I had to show that even if you continued, it is impossible. Specifically, I have said "This is impossible to complete because no matter how many 0's you add, you will never reach 15 which is another reason why it is impossible to complete a division by 0." I have clearly stated "you will never reach 15" and that's because it just isn't possible or "undefined".

In the previous examples that I have done,15"5 = 5+5+5, and 15"3= 3+3+3+3+3, the numbers add up. 5+5+5 = 15, 3+3+3+3+3 = 15. This is why the equation is true in both theory and practice. However, with your thinking, even if you add an infinite amount of 0's, the numbers will still not add up, 0+0+0+0+0+0+0+0+0+0+0+0+0+0......+0+015 no matter how many 0's you add. This is not a matter of "because it doesn't end, it is infinity." That is why everyone knows there is a difference between "never" and "in a while". 0+0+0+0+0 will never yield the total of 15 or any number other than 0. 0+0+0+0+0 will not yield the total of 15 just because you add 0 for a few thousand years or even infinity. You have to understand that it's just not possible.
15/3= 3+3+3+3+3
You add 3 five times, therefore the answer is 5.
15/5 = 5+5+5
You add 5 three times, therefore the answer is 3.
15/0 = 0+0+0+0+0,
You add 0 but it is not infinity because no matter what number of zeros, even , you still won't arrive at 15. So the conclusion we arrive at is :there is NO number of 0's in which you can add to 0 in order to make 0 turn into zero. This is why it is safe to say it is undefined (no number possible).

And finally we can say that the number of 0's required to get from 0 to 15 is undefined, because there is no number which does so.

Fourthly, the fallacy is completely relevant. Without the impossibility of dividing by zero, using that procedure, we proved that 1=2. The only reason of why 1 does not equal 2 in the mathematical universe is because you cannot possibly divide by zero, shown in the mathematical fallacy. Can you find another reason why 1 would not equal 2? No because the sole reason is because you cannot divide by 0.

Now, Logical : adjective \;l"-ji-kəl\
1.Capable of reasoning or of using reason in an orderly cogent fashion
2.Based on earlier or otherwise known statements, events, or conditions; reasonable
3.Reasoning or capable of reasoning in a clear and consistent manner.

Sources :
http://www.thefreedictionary.com...
http://dictionary.reference.com...
http://www.merriam-webster.com...

Now, just because it is logical (reasonable), it does not mean it is possible in theory. All that I have said is that your evidence was thought out and understandable. It could still be right or wrong, and in this case, your theory is wrong. That is why it not possible, even in theory.

In the beginning you said that 0 is impossible to completely reach.
But later on you said :
"5 / =0
Than...
5 / 0 ="
To summarize, this was all that your theory consisted of. Put in simpler terms, "because we assume 5 / =0, we can assume that using basic algebra, 5 / 0 =".
But you have stated that reaching 0 is impossible in your first few paragraphs, as I have stated in round 2. How could 5 / =0 in your own theory if you yourself said that "it's impossible to reach Zero without jumping numbers, is that counting down, you will find yourself counting forever"?

I would like to remind you that I have completely rebutted against your points. Refer back to my round 2 argument where I say:
"First off, I would like to bring up a contradiction in your theory. You said that"Zero is can't be reached, because unlike the other Whole Numbers, it's amount is infinitely small". Then, in the second part of your theory, you said that"5/=0", now isn't that a bit contradicting?" and the entire paragraph after that.

My 4th argument could be ignored but there is still irrefutable evidence against you.
Debate Round No. 3
33 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Irresistable 3 years ago
Irresistable
Lol?
Posted by donald.keller 3 years ago
donald.keller
So according to high level math.. I was right, X / 0 = infinity...... Well :D Damn straight!
Posted by kazmo 3 years ago
kazmo
There is only one instance where you are able to divide by 0, it is in an extended complex plane. But that involves "complex infinity" and it is very difficult to understand. I'm pretty sure it's extremely high level math. A site which helps : http://mathworld.wolfram.com...
Posted by donald.keller 3 years ago
donald.keller
Thank you :) I will look into Calculus when I have some time.
Posted by Juan_Pablo 3 years ago
Juan_Pablo
Well, donald, you might be onto something. I recommend you investigate it more.
Posted by donald.keller 3 years ago
donald.keller
Lol XD
Posted by Shadowguynick 3 years ago
Shadowguynick
I know, it was just funny how it was worded XD
Posted by donald.keller 3 years ago
donald.keller
Lol Shadow. I was saying could work in theory, but only in theory. XD
Posted by donald.keller 3 years ago
donald.keller
lol Ya.. I really wanted to debate you on this. Oh well lol. Remember to vote.
Posted by Shadowguynick 3 years ago
Shadowguynick
Lol, I'm sorry I didn't get to debate you donald. I posted the comment, and then totally forgot XD. I wish DDO would remind us about comments on debates we comment on.
7 votes have been placed for this debate. Showing 1 through 7 records.
Vote Placed by countzander 3 years ago
countzander
donald.kellerkazmoTied
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Reasons for voting decision: It is theoretically possible to divide by zero, just not under the set of real numbers. Pro should have appealed to complex numbers.
Vote Placed by rajun 3 years ago
rajun
donald.kellerkazmoTied
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Reasons for voting decision: Con had more convincing arguments while arguments from pro such as "Zero can' be reached" made no sense to me. Con wins this one because of his convincing argument by showing that division is multiple subtraction and no matter what, 15 can't be got to 0 by subtracting 0 from it...infinite times.
Vote Placed by Juan_Pablo 3 years ago
Juan_Pablo
donald.kellerkazmoTied
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Reasons for voting decision: Ultimately I gave a 3 point win to Con on the basis of his arguments. They made more sense and ultimately convinced me of his position at the end. As for the possibility of Pro's resolution, I guess it's possible if he works on them and even invents a new math or something. I don't want to suggest that something like this isn't possible because it still might be, but Pro will have to play with this idea until he can present an argument to show why it should be taken seriously. I would recommend researching calculus (as the subject deals with infinities) and finding news ways of expressing infinities in a rational, useful way. For example, in Calculus it's possible to break a quantity up into an infinite number of fractions. Perhaps he can show that every real number (quantity) is implicitly a unique infinity - and that infinities can thus be compared as the rational, real numbers they take on ( 1 = 1 infinity, 6 = 6 infinity). I think donald might be onto someting.
Vote Placed by Shadowguynick 3 years ago
Shadowguynick
donald.kellerkazmoTied
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Reasons for voting decision: Kazmo's arguments were more convincing overall, and applied more mathematical arguments. Plus pro's definition of theoretical seemed contradictory. Could work, but doesn't work? I don't know about that.
Vote Placed by guesswhat101 3 years ago
guesswhat101
donald.kellerkazmoTied
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Reasons for voting decision: While Pro has some interesting ideas and theories, his arguments were too weak to beat Con. Con didn't have to back up why you can't divide by zero but he did and very well I might add. I had a major issue with Pro's idea of infinity, especially in the final round where he treated Infinity as a number (albeit never-ending).
Vote Placed by RoyLatham 3 years ago
RoyLatham
donald.kellerkazmoTied
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Reasons for voting decision: The argument that zero "cannot be reached" because it is infinitely small makes no sense. It's reached the same way all the other numbers are reached. "Theoretically possible" means that there is a valid theory that does not lead to a contradiction. Con showed that Pro's examples lead to contradictions. Con should have also used an expert opinion, like a math textbook, but it wasn't necessary.
Vote Placed by wiploc 3 years ago
wiploc
donald.kellerkazmoTied
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Reasons for voting decision: Con was lucid and cogent. Pro was confusing and contradictory. S&G: Pro was often difficult to comprehend.