The Instigator
LR4N6FTW4EVA
Pro (for)
Losing
0 Points
The Contender
Lightkeeper
Con (against)
Winning
21 Points

A number divided by zero has l00l.

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Post Voting Period
The voting period for this debate has ended.
after 4 votes the winner is...
Lightkeeper
Voting Style: Open Point System: 7 Point
Started: 10/11/2008 Category: Miscellaneous
Updated: 8 years ago Status: Post Voting Period
Viewed: 2,285 times Debate No: 5672
Debate Rounds (3)
Comments (20)
Votes (4)

 

LR4N6FTW4EVA

Pro

Okay, check this out: 1/1=1, 1/.1=10, 1/.01=100, 1/.001=1000

So basically, as the denominator approaches zero, the absolute value of the fraction equals infinity. That means that 1/0=00 (that's an infinity sign).

This principle is applied elsewhere in mathematics. For example, as the amount of 9's in the series .9, .99, .999... approaches 00, the value of the decimal approaches one. Mathematicians use this logic to show that .999...999=1. This applies to number x/0.
Lightkeeper

Con

x/0 cannot be equal infinity in as much as 1 cannot equal 2, 1000 cannot equal Pi, 0 cannot equal -3029133

if a/b=c then c*b=a

if x/0=infinity then infinity*0=x

Substitute 1 for x and we get:
if 1/0=infinity then infinity*0=1

Now substitute 2 for x and we get:
if 2/0=infinity then infinity*0=2

If infninity*0=1 AND infinity*0=2 then 1=2

But 1 does not equal 2

Therefore x/0 cannot equal infinity
Debate Round No. 1
LR4N6FTW4EVA

Pro

Good argument. However, I will not go down that easy.

My opponent's mathematics show that the principle that I set forth is counterintuitive.
I respectfully disagree.

Infinity, because it is not a specific number will provide an exception to the rule. For example x/7
But when it comes to infinity, things change. 00/7=00

It's the same with zero. 0/7=0

Zero and infinity are the two odd fellows, because both break the general rules of math.

For example, 2=/=x, but if x is 0 or 00, this isn't true.

That means that there is an exception to the rule my opponent listed.
Lightkeeper

Con

My opponent's response now is that ordinary mathematics (such as "if a/b=c then c*b=a") do not apply to his proposition because both infinity and zero are odd fellows.

With respect, my opponent wants to have it "both ways". He wants to have his cake and eat it too (for want of a better expression). You see, division is defined as follows:

"To divide a number a by another number b is to find a third number c such that the product of b and c is a, that is, b � c = a. The number a is called the dividend, the number b is called the divisor, and the number c is called the quotient. The operation of dividing may be denoted by a horizontal or diagonal slash separating the dividend and divisor (with the dividend on top), or by a horizontal dash with a dot above and below it placed between the dividend and divisor."(http://www.mathacademy.com...)

"A basic arithmetical operation determining how many times one quantity is contained within another. " (http://www.mathpropress.com...)

"In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication." (wikipedia)

"Mathematics The operation of determining how many times one quantity is contained in another; the inverse of multiplication. " (American Heritage Dictionary at www.dictionary.com)

All the above definition are, in my submission the same in effect. They say that division is the inverse of multiplication. Therefore by definition if a/b=c then c*b=a. Any position inconsistent with that is not a division.

Now of course, my opponent is free to devise a new mathematical system. Indeed, he is free to devise a system where 1+1=3. There is nothing to stop him from that.

However, he has not stipulated in his first round or in his resolution that he has some new unknown meaning of "division" in mind and has not provided any new definition.

Therefore, on one hand, he proposes that we apply standard mathematics (the very process of division) to a division by zero and hence obtain the result "infinity". On the other hand, he claims that division by zero is not subject to standard mathematics. He has not provided any evidence or reasoning to support this latter contention, other than simply agreeing that standard mathematics cannot apply to his proposition because standard mathematics would not support it.

On an intuitive level, we can imagine division as this:
By dividing one number by another we work out how many of the latter will exactly fit in the former.
How many zeroes will make number x?
"Infinity of zeroes" we hear my opponent shout.
And yet we know that zero multiplied by any number at all gives us.... big fat zero.
That's because an infinitely big set of nothings is still full of nothing.
Again, this is intiuitive thinking based on standard mathematics. I am aware that my opponent will challenge this by saying that he's already contended that standard maths do not apply to his proposition. However, I still wanted to put this reasoning here just to assist those who might prefer a more practical approach to purely theoretical maths.

BOTTOM LINE
I conclude that my opponent's resolution cannot succeed because the result he obtains from his process is contradictory to the very definition of the process (the process being division).
Debate Round No. 2
LR4N6FTW4EVA

Pro

My opponent misinterpreted me.

I said that it didn't work because 00 is not one single number.

Under that principle, we find that the mathematics he used won't work as a disproof.
Lightkeeper

Con

My opponent now claims that I have misintepreted him. I contend that I did not.

Furthermore, and more importantly, I stated that my opponent's proposed division of x/0=00 is not a division at all, since division is defined as the inverse of multiplication. Thus, a/b=c can't be true unless it is true that c*b=a. That is the definition of division and the division proposed by my opponent is contradictory to this definition. Please note that my opponent has not even addressed this argument in his last round.

I will point out further that ANOTHER division proposed by my opponent may well be valid. He proposed that 00/x=00. That would be true as 00*x=00 (infinity times x = infinity). However, that does not apply to x/0. If x/0=00 then 00*0 would have to equal x. This would only be potentially true in a case where x was equal to zero. However, on closer examination, even if x were equal to zero, the same problem would arise. The division could not return any number c. Why? Here's why:
a/b=c then c*b=a
0/0=0 therefore 0*0=0 (all good so far).
but
0/0=1 therefore 1*0=0 (also true)
0/0=1010 therefore 1010*0=0 (equally true)
0/0=-10191 therefore -10191 *0 = 0 (and that's true too)
Hence even where x is zero, it can't be divided by zero as this would to an obvious contradiction. You see, if 0/0=1 and 0/0=2 and 0/0=3 etc... then 1=2=3=.........

Have I misinterpreted my opponent? I said that he contends that zero and infinity are odd fellows. Please see his previous post and you will in fact find that contention. In the final round he seeks to clarify that contention by providing his reasoning for it. He says that infinity and zero are odd fellows because infinity is not a single number. That's all well and good. Let us briefly revisit the definition of division:

"To divide a number a by another number b is to find a third number c ..."

If infinity is not a single number then can it ever be found to constitute the "third number c" in the above definition? I say it cannot. It cannot because a "third number c" is a "single number". Number c is such a number that, if multiplied by b it will give us a. By my opponent's own admission, that does not apply to infinity.

It is my conclusion that my opponent has not proven his resolution. His process of division was contradictory any known definition of division. A division by zero is undefinable simply because it would need to entail the finding of a number c such that if multiplied by b it gives x. No such number exists except where a is also 0.

You should therefore vote Con.

I thank my opponent for this debate.
Debate Round No. 3
20 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Lightkeeper 8 years ago
Lightkeeper
VenomousNinja

It could not be won on that question. Read the debate. Or open a dictionary to see how division is defined.

LR4N6FTW4EVA

You are justified :)
If you actually resolved that in the R sphere there is a limited application of a concept of division by zero then I wouldn't even debate you. I don't understand R sphere. I'm not sure if anyone does, other than R himself.
Posted by VenomousNinja 8 years ago
VenomousNinja
I haven't read the debate, but I know that this could be won with one question:
"How many times can you fit nothing(0) into a box?"
The answer is endless times. Thus, you would easily win.
Posted by LR4N6FTW4EVA 8 years ago
LR4N6FTW4EVA
\infty is supposed to be the infinity sign
Posted by LR4N6FTW4EVA 8 years ago
LR4N6FTW4EVA
"On the other hand, this kind of infinity enables division by zero, namely z/0 = \infty for any complex number z. In this context is often useful to consider meromorphic functions as maps into the Riemann sphere taking the value of \infty at the poles. "

I feel justified now!
Posted by Lightkeeper 8 years ago
Lightkeeper
LOL Puck.... what you've written looks familiar... very familiar.... eerily familiar :P
Posted by LR4N6FTW4EVA 8 years ago
LR4N6FTW4EVA
I see. I tried this debate with a limited amount of mathematical knowledge (I'm in Pre-Calc), and obviously I got beaten. Thanks for the explanation, both of you.
Posted by Puck 8 years ago
Puck
&#8220;Infinity, because it is not a specific number will provide an exception to the rule. For example x/7<x is certainly true.&#8221;

You attempt to introduce a new element &#8220;infinity&#8221; which you want to append to the real number system. Note this is not prohibited. After all, that is how we got from natural numbers to integers > rationals > reals > complexes. However you end with something that is not the real number system.

Some of these work fine.
infinity + X = X + infinity = infinity
(-infinity) + X = X + (-infinity) = -infinity
infinity + infinity = infinity

Where the trouble is, is with defining the following:
infinity + (-infinity)
(-infinity) + infinity
infinity - infinity
(-infinity) - (-infinity)
0 * infinity
infinity * 0
0 * (-infinity)
(-infinity) * 0
infinity / infinity
infinity / (-infinity)
These expressions are called "indeterminate forms." They can all have a large range of different values, depending on exactly where the "infinity" parts came from.
As a result, the system constructed is not closed under addition, subtraction, multiplication, or division.
Posted by Puck 8 years ago
Puck
1/0 is held to be undefined because division is defined in terms of its multiplication counterpart.
a/b = x is b*x = a. There is no possible x where that 0*x = 1, since 0*x = 0 for _all_ x. Therefore 1/0 does not exist and instead remains as undefined.

There is an axiom in mathematics: a(b/a) = b
For example; 1/0 = 2, 0(1/0) = 0*2 = 0 doesn't work, so you could never use the rule. You are in essence saying we should change mathematical rules to make an exception for 0. To do that however you would need to make every rule to specifically say that it doesn't work for zero in the denominator, so what's the point of making 1/0 = 2 in the first place? You simply can't use any rules on it.

Why it can&#8217;t be: 1/0 = infinity.
Does infinity - infinity = 0?
Does 1 + infinity = infinity?

However that fails too as, (a+b)+c = a+(b+c) will not always work:
1 + (infinity - infinity) = 1 + 0 = 1, but
(1 + infinity) - infinity = infinity - infinity = 0.

You can attempt to make up a new set of rules, but it always leads to errors which is why it is regarded as undefined.
Posted by Lightkeeper 8 years ago
Lightkeeper
Rezzealaux
Riemann sphere has a very limited application and certainly was not part of this debate :)
If you understand Riemann sphere then you should start a debate on it. I personally don't understand it. But looking at wikipedia it has some limited application under some specific circumstances and has absolutely nothing to do with this debate or any of the arguments herein :)
Posted by Lightkeeper 8 years ago
Lightkeeper
Hmmm all normal on my screen....
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Vote Placed by Zerosmelt 8 years ago
Zerosmelt
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Logical-Master
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