Challenging the Conventional: Divide by Zero

[Fiendish_Dire_Moose]

(I'm in math 94, so this may not apply to those of you more math savvy.)

Math, the single universal truth in the world. We made it, and we applied it, and guess what, it worked. It was provable, understandable, and teachable. But as time went by, it became more complex. As technology grew we found ourselves needing math more and more.
What started out as 2+2=4, became 2x+4(3x-2)=x7-(34-x). And it didn't stop there. Math gave us science, and science served to further our technology even greater. But in this single great universal truth there is the single greatest lie teachers tell their students. This lie of course, is that dividing by zero, is undefined.
Let's take what we know first and foremost about division. Division is two things, it's repeated subtraction, and it is multiplication reversed. And these statements are truth. To multiply anything by zero, gets a result of zero. To subtract zero from anything, get a result of the original numerals.
So why does dividing by zero get an undefined result? The simple answer is that a number cannot go into zero. So then how does that make it undefined?

Zero=nothing. No capacity to hold numbers, no capacity to go into a number. So if we take what we know about zero, and divide a number into it, shouldn't the result simply be zero? Of course it should.
How many times can nothing go into 1,645? None. Zero will go into this number, zero times.
How many times can 45 go into nothing? None. A number multiplied by zero, is zero, so dividing the same number by said nothing, is nothing. You cannot fit 45 oranges into a cylinder if it is unable to hold anything.
So, ladies and gentlemen, the next time your math teacher tells you that dividing by zero is undefined, challenge him/her, and call them out for their lies. And when you do, quote Big Boss with, "All things return to Zero."

[Eldan]

Welll, look at it like this.
As my teacher once explained: to divide 100 by five, imagine one hundred peas. Divide them on five stacks.

Now take the 100 peas and make 0 stacks out of them. (Assuming that every pea has to be in a stack.)


Or: You say that 0 can go into 1645 0 times. Really? You have an empty bath pool which can hold 1645 litres and a (rather strange) bucket holding 0 litres. How many times can you empty it into the pool before the pool is full?

Edit:
Also, for "division is the reverse of multiplication": multiplying both sides of an equation by zero is, as far as I remember, also an illegal operation.

[BritishBill]

Big Boss is the man.

[SurlySeraph]

Also, for "division is the reverse of multiplication": multiplying both sides of an equation by zero is, as far as I remember, also an illegal operation.

This is correct.

Also, I advise you to repent of your heresy before the Mathquisition finds out.

[Solaris]

... Also, the sun is shiny, water is wet, and air is breathable.

[Douglas]

This is correct.
Actually, it isn't. Multiplying both sides of an equation is a perfectly valid operation that will give you a valid equation. It just won't be very useful because it is trivially true and if it's an algebraic equation you're trying to solve you will find that all possible values you could substitute in will all work.

[Thatguyoverther]

I always tended to think of it as you would get a number so astronomically high, it breaks reality.

Like if you divide 2 by .1 you get 20. And 2 by .00000000001 you get two hundred billion, except 0 is infinitely smaller than .00000000001 giving you an infinite-ish number.

It's been a while since my last Calc, class, but it think you do start dividing with zero when you get into limits.

[Pyrian]

Multiplying both sides of an equation is a perfectly valid operation that will give you a valid equation.Not really. Or, rather, that's not sufficient to make the operation valid. The point of multiplying both sides of an equation by the same thing is that you get the same equation. This is not true if you use zero; you no longer have the same equation.

Thus,

1=2
0x1=0x2
0=0
Ergo,
1=2

[Cubey]

Also, I advise you to repent of your heresy before the Mathquisition finds out.

Too late, we're already here.

If a/b=c, then b*c=a.

So by the OP's logic:
100/0 = 0
0*0 = 100?

Makes no sense. And it's nothing math savvy either. I just debunked this theory with grade school material.

[Telonius]

Zero=nothing. No capacity to hold numbers, no capacity to go into a number. So if we take what we know about zero, and divide a number into it, shouldn't the result simply be zero? Of course it should.
How many times can nothing go into 1,645? None. Zero will go into this number, zero times.
How many times can 45 go into nothing? None. A number multiplied by zero, is zero, so dividing the same number by said nothing, is nothing. You cannot fit 45 oranges into a cylinder if it is unable to hold anything.
So, ladies and gentlemen, the next time your math teacher tells you that dividing by zero is undefined, challenge him/her, and call them out for their lies. And when you do, quote Big Boss with, "All things return to Zero."

The flaw is in bold. Zero will not go into the number, zero times; because zero will not go into the number at all. It's the same thing as asking how many times zero will go into banana. The answer isn't zero, it's the null set.

[Tirian]

Not really. Or, rather, that's not sufficient to make the operation valid. The point of multiplying both sides of an equation by the same thing is that you get the same equation. This is not true if you use zero; you no longer have the same equation.

Thus,

1=2
0x1=0x2
0=0
Ergo,
1=2

Not really. If a = b, then ac = bc for any c. Indeed, f(a) = f(b) for any well-defined function f, including constant functions. There is no necessity that the function be invertible.

What you entered here is a valid proof that 1=2 implies 0=0, and that is a true statement. You can imply anything from a false hypothesis; the hypothesis doesn't become true just because you derived a true statement from it.

[Pyrian]

Perhaps I am using the wrong terminology.

How would you choose to describe the fact that the condition if(a==b)==if(ac==bc) for all a & all b where c <> 0?

[Douglas]

What you have illustrated is that multiplying an equation by 0 is not a reversible operation. Most algebraic manipulation is done with a goal in mind that requires that going through the exact same sequence of steps backwards would be valid. While multiplying an equation by 0 is valid, factoring out (or dividing by) 0 is not. This makes it valid but generally useless.

[Kobold-Bard]

...Or: You say that 0 can go into 1645 0 times. Really? You have an empty bath pool which can hold 1645 litres and a (rather strange) bucket holding 0 litres. How many times can you empty it into the pool before the pool is full?...

Broken bucket with no bottom?

[Tirian]

(warning: this is far afield. And, while I'm not making up these words, I am pulling them out of my hat in a way that others might not.)

Saying that a=b implies ac = bc for all a, b, c -- that would be sort of a Substitutivity of Identity, which is a part of meta-mathematical logic. Basically, if you have two different expressions that both refer to the same mathematical object, then they are interchangeable. This is always true.

The opposite, that ac = bc implies ab for all a, b, c -- in abstract algebra that is called the solvability criterion, and a function f that satisified f(a) = f(b) implied a=b would be called injective (or one-to-one). It is true for some algebraic structures (like addition of numbers or multiplication of non-zero numbers) but not for others (like multiplication of matrices or composition of functions). Here, you've got to take a step or two to justify your logic if you want to "undo" a function on both sides of an equation.

Long story short, someone was right below when they said that there is no reason why you couldn't multiply both sides of an equation by zero but also no reason why you would want to.

[Arutema]

(I'm in math 94, so this may not apply to those of you more math savvy.)

If you want to get fully into the topic of division by zero, I would suggest you continue on to Calculus, where the subject is discussed in some depth.

I do not have the time to summarize the rationale here, but a result of x/0 can be considered infinite, negatively infinite, or an invalid result depending on the application.

[Solaris]

Too late, we're already here.

Nobody expects the Mathquisition anymore.

[valadil]

If you want to get fully into the topic of division by zero, I would suggest you continue on to Calculus, where the subject is discussed in some depth.

I do not have the time to summarize the rationale here, but a result of x/0 can be considered infinite, negatively infinite, or an invalid result depending on the application.

I have the time though! Well, at least the time to get people started on the very basic intro to calculus.

Start with a graph. We're going to graph what happens when you divide by different numbers. Lets say our number n is 100. We'll divide it by a number x. x is going to decrease, but lets start it at 10 for argument's sake. 100/10 is 10, so mark 10,10 on your graph. Then let x equal 9. 100/9 is a little over 11. So mark 9,11.something on the graph. Then 8,12.25; 7,14.and_change, etc down to 1,100. Next would be 0, but we don't know how to divide by 0. Instead graph .1. Then .01, .001, etc. x gets smaller (as it approaches 0) your result gets bigger (it approaches infinity). That's calc in a nutshell.

[Lappy9000]

Mah head dun gone an' hurt (http://cdn1.knowyourmeme.com/i/2355/original/DivideByZero.jpg).

You dang mathematicians are responsible for far too much head-asplodey! :smallmad:

[Groundhog]

I always tended to think of it as you would get a number so astronomically high, it breaks reality.

Like if you divide 2 by .1 you get 20. And 2 by .00000000001 you get two hundred billion, except 0 is infinitely smaller than .00000000001 giving you an infinite-ish number.

It's been a while since my last Calc, class, but it think you do start dividing with zero when you get into limits.

Yes, that's how I always thought of it. It's not so much undefined as infinitely small.

[RS14]

Let me point out that a/0=0 suggests that a=0*0, which is nonsensical.

Edit: Sorry Cubey, I now notice that you said essentially the same thing.

[AtomicKitKat]

I've said it before(since back in the 1990s), and I will say it again. Division by zero produces a triple-state figure. It is simultaneously both 0, and the original numerator, and infinity. Think of it along the same Heisenburg's uncertainty principle. You can empty your 0-litre bucket an infinite number of times into the pool. Likewise, you cannot take any water out of the pool with your flat "bucket". In the case of 0/0, it is still triple-state, as the answer is also 1, in addition to 0(the original numerator) and infinity). Understanding how this can be so is somehow beyond the capabilty of most people.:smallcool:

[bluewind95]

I've said it before(since back in the 1990s), and I will say it again. Division by zero produces a triple-state figure. It is simultaneously both 0, and the original numerator, and infinity. Think of it along the same Heisenburg's uncertainty principle. You can empty your 0-litre bucket an infinite number of times into the pool. Likewise, you cannot take any water out of the pool with your flat "bucket". In the case of 0/0, it is still triple-state, as the answer is also 1, in addition to 0(the original numerator) and infinity). Understanding how this can be so is somehow beyond the capabilty of most people.:smallcool:

For the bucket analogy... I get how it is both 0, and infinity. But... the original numerator? Can you please elaborate for this math-disabled person?

[Fiendish_Dire_Moose]

Too late, we're already here.

If a/b=c, then b*c=a.

So by the OP's logic:
100/0 = 0
0*0 = 100?

Makes no sense. And it's nothing math savvy either. I just debunked this theory with grade school material.

I have no recollection of typing ANYTHING close to 0*0=100. At all. What I said was any number*0 is zero. So, no, you didn't debunk anything, you drew a completely BS conclusion.
The idea that a*0=0, ergo 0/0=A is following the idea that division is reverse multiplication. Which it is, the rules however curve themselves. That's kind of how Algebra works. One thing won't always mean the opposite.
Like today I learned that the square root of -64 is not a real number, yet my friend learned in his super math that it in fact is. That's just a higher math. The rules are different, but the result wills till be the same.

[Zeb The Troll]

I have no recollection of typing ANYTHING close to 0*0=100. At all. What I said was any number*0 is zero. So, no, you didn't debunk anything, you drew a completely BS conclusion.Well, according to what I learned in Algebra I, the math he posted directly correlates to what you declared in the first post. I'm not sure how you don't see that.

If a/b=c ({any number}1/0 = 0) then b*c=a (0*0 = [1645])

1Let's use 1645 since it's the one you used.

I can't speak to any of this higher math discussion because a. I never learned it and b. even if I did, I've since forgotten. But I do know that algebraically he did not mispresent what you said.

EDIT: Wait, you edited that after I quoted it, but what I recall from my high school math classes is that yes, one of the basic tenets of math (or at least algebra) is that if its correct, it's reversible. That's how they taught us to check our work. The fact that -641/2 equals 8i doesn't change that, because 8i squared is -64.

[RS14]

The idea that a*0=0, ergo 0/0=A is following the idea that division is reverse multiplication. Which it is, the rules however curve themselves. That's kind of how Algebra works. One thing won't always mean the opposite.

Then you're using an operation of your own devising, call it &. But division by some q is defined as multiplication by the multiplicative inverse of q. And this definition is useful.

0*0=100 follows logically from your assertion and from a/b=c implies a=b*c, which itself follows from the above definition of division, in the special case that a=100, b=c=0. Either your assertion is false, in which case we accept that a/0 =/= 0, or a/b=c implies a=b*c is false, in which case we accept that division by zero is undefined.

I would also like to note a general trend:

100/100=1
100/10=10
100/1=100
100/(1/10)=1000
...

If nothing else, note that your definition runs contrary to the general trend.

[Fiendish_Dire_Moose]

If nothing else, note that your definition runs contrary to the general trend.
*Looks at title of thread*
I don't know if I can do that :smallamused:.

[Tengu_temp]

So, no, you didn't debunk anything, you drew a completely BS conclusion.


Way to be passive-aggressive there. Not to mention that what he said was a completely logical proof to why your hypothesis is wrong. The "super math" you mention are imaginary numbers, and they follow the same rules for simple math operations as real numbers.


*Looks at title of thread*
I don't know if I can do that :smallamused:.

I don't see how making your own definitions of things suddenly challenges conventional math, or proves it to be wrong.

[Fiendish_Dire_Moose]

Way to be passive-aggressive there. Not to mention that what he said was a completely logical proof to why your hypothesis is wrong. The "super math" you mention are imaginary numbers, and they follow the same rules for simple math operations as real numbers.
It's "wrong" because math books tell you it's wrong. The point of it is not whether it's right in the books or not, but WHY it's right/wrong.
There is no right here.
Logically x/0= infinite/undefined.
But logically as well if 0=nothing, than anything/0=0.



I don't see how making your own definitions of things suddenly proves conventional math to be wrong.

I didn't say it did. Perhaps you should read what I was replying to with that.

[AtomicKitKat]

For the bucket analogy... I get how it is both 0, and infinity. But... the original numerator? Can you please elaborate for this math-disabled person?

Ahh. The reason it is simultaneously the numerator, is because when you attempt to exert a non-effective force(in this case, your flat bucket, or "0") upon the pool(the numerator), the pool still exists.

Ergo:

0/0=1 or 0 or infinity.
X/0=X, 0, or infinity.

0 is both all powerful, yet null. Sort of a black hole thing. To explain more would involve possibly religious connotations.

[Fiendish_Dire_Moose]

0 is both all powerful, yet null. Sort of a black hole thing. To explain more would involve possibly religious connotations.
I can do it while avoiding religion: /0 is Windows ME. A great OS, if it wouldn't crash during boot up.

[Tengu_temp]

It's "wrong" because math books tell you it's wrong. The point of it is not whether it's right in the books or not, but WHY it's right/wrong.
There is no right here.
Logically x/0= infinite/undefined.
But logically as well if 0=nothing, than anything/0=0.

...
You were just proven why you're wrong, not by math books, but by logical arguments. And you called that proof "a completely BS conclusion". Why do you want to spark a discussion, if you don't listen to counterarguments?



I didn't say it did. Perhaps you should read what I was replying to with that.

Then I have no idea what you meant there.

[Fiendish_Dire_Moose]

...
You were just proven why you're wrong, not by math books, but by logical arguments. And you called that proof "a completely BS conclusion". Why do you want to spark a discussion, if you don't listen to counterarguments?

Whether or not it is "proof" is strictly undeniable, and BESIDE the point. Yes it "logically" makes sense.
If ax0=0, then 0/a=a and what not. But whether or not it is actually logical is the question. If 0 can't go into anything, how can anything go into 0?
And once again, it only makes sense because that is how we learned it. If you were taught from day 1 that automobiles ran on faerie dust, you'd believe it to make sense. You'd still be wrong. But once again, it's not about right or wrong. It's about logic, and if it's truly logical for the single reason that we're told it is.



Then I have no idea what you meant there.
He/she said I needed to at least admit my argument was contrary to the current trend. The thread title is "Challenging the conventional", IE: challenging the trend.

[Tengu_temp]

So do you have any actual arguments other than "what we were taught is wrong"? Because I don't call that challenging the conventional, I call that trying to be different just because. Just like Tengu, 5-year old, who insisted that the next (natural) number about nineteen is not twenty, but "tenteen", and twenty is after that (he quickly grew out of it, luckily).

Also, look up logic on wiktionary. I don't think it means what you think it means. Heck, let me do it for you: here (http://en.wiktionary.org/wiki/logic).

[Zeb The Troll]

He/she said I needed to at least admit my argument was contrary to the current trend. The thread title is "Challenging the conventional", IE: challenging the trend.No, he said you should note that your definition is contrary to the general trend.

[Fiendish_Dire_Moose]

So do you have any actual arguments other than "what we were taught is wrong"? Because I don't call that challenging the conventional, I call that trying to be different just because. Just like Tengu, 5-year old, who insisted that the next (natural) number about nineteen is not twenty, but "tenteen", and twenty is after that (he quickly grew out of it, luckily).

Also, look up logic on wiktionary. It doesn't mean what you think it means.
If you find nothing worth discussing then you are welcome to leave. I take no pleasure in arguments and prefer discussions.

And to humor you: Logic: the science that investigates the principles governing correct or reliable inference.

Now that that is out of the way. We find it logical, because we were taught that it is. Math may be a universal truth in application, but it was in fact invented by people, passed down by people, and is practiced by people. So, if I feel there is a flaw, I'm very much well within my humanly rights to question it.
There is literally no change to the result if we simply restate it as zero. Building won't collapse, bridges won't give way under their own weight, and out space shuttles will explode 70 seconds after launch, just as much.


No, he said you should note that your definition is contrary to the general trend.

Is there a difference? My argument would be my definition would it not?

[Serpentine]

Zero goes into anything infinite times. Anything divided by zero is infinity. Infinity is very difficult, if not impossible, to apply to anything lower than very high mathematics, therefore at lower mathematics it's declared, for practical purposes, impossible.

There :smallcool:

[Tengu_temp]

There is literally no change to the result if we simply restate it as zero. Building won't collapse, bridges won't give way under their own weight, and out space shuttles will explode 70 seconds after launch, just as much.


Not instantly, but in the future many calculations where 0 is included will bring wrong results. Some of those calculations would be made to ensure that the building won't collapse, or that the shuttle won't explode.

[Fiendish_Dire_Moose]

Not instantly, but in the future many calculations where 0 is included will bring wrong results. Some of those calculations would be made to ensure that the building won't collapse, or that the shuttle won't explode.

Quite possibly, but honestly, I can never see where /0 would not equal zero being important.
Space shuttles for one requiring precise calculations that do require specific accurate definition.

@Serpentine: So basically it's the square root of -64, and don't nobody tell me that that = -8i without defining i.

[Serpentine]

It's of the same variety more or less, yes.

I can't think of any specific examples, but I have no doubt that there are definitely places where it is very important that /0 = infinity, NOT 0.

[daggaz]

So he refuses to use logic unless its his logic, and reverts to passive aggressive flaming ("your post is bs" and we all know what bs means) when proven unaquivacably wrong.

Dont feed the math troll, guys.

By the way, the 0*0=/=100 (or any other number) was the most eloquent and simple proof I have seen as to why dividing by zero does not equal zero. I am going to start using it when teaching my own students (I do one on one intensive lessons for remedial math students).

I usually pointed it out by having a student divide a number by increasingly smaller numbers. The answer gets bigger and bigger and bigger...why should it suddenly flip over to zero? But limits can be confusing for some people.

[Tengu_temp]

Quite possibly, but honestly, I can never see where /0 would not equal zero being important.
Space shuttles for one requiring precise calculations that do require specific accurate definition.


Let's say we make a hut on poles, and somehow we devise it without any poles. The hut weights X, a single pole can only support Y weight before breaking. How much weight each pole is holding?

Scenario 1: normal math. Each pole is supporting X/0 weight, which means... oops, impossible, back to the drawing board!
Scenario 2: your math. Each pole is supporting X/0 weight, which means 0, which means the plan is fine because 0 < Y. Proceed with construction!

[Fiendish_Dire_Moose]

So he refuses to use logic unless its his logic, and reverts to passive aggressive flaming ("your post is bs" and we all know what bs means) when proven unaquivacably wrong.

Dont feed the math troll, guys.

Right, so just because I calling out the standard logic I refuse to use it? The current logic presented is /0=infinite, yet the only reason I'm given is, "Because".
The "logic" I'm handed is nothing more than being told that's just the way it is, with no real why.

If I'm a troll for calling the previous conclusion about my post BS, then you're a troll for posting that I am one. See where this is getting us?

[Fiendish_Dire_Moose]

Let's say we make a hut on poles, and somehow we devise it without any poles. The hut weights X, a single pole can only support Y weight before breaking. How much weight each pole is holding?

Scenario 1: normal math. Each pole is supporting X/0 weight, which means... oops, impossible, back to the drawing board!
Scenario 2: your math. Each pole is supporting X/0 weight, which means 0, which means the plan is fine because 0 < Y. Proceed with construction!

No, my scenario still states that each pole will support zero weight, as they aren't existent. The number of poles is factor P. X/(0P). P=0 in this case. 0 poles means 0 weight is supported which means the hut has nothing to stand on. X/(0P)= X/(0*0), so dividing X by 0 means that there is nothing to support the weight.

[Tengu_temp]

Right, so just because I calling out the standard logic I refuse to use it? The current logic presented is /0=infinite, yet the only reason I'm given is, "Because".
The "logic" I'm handed is nothing more than being told that's just the way it is, with no real why.


Actually, you were given a lot of viable, non-"because" arguments. Do you want me to quote them?


No, my scenario still states that each pole will support zero weight, as they aren't existent.

Er, that's what I just said. Each pole will support 0 weight, and since they're designed to support up to Y weight, it means their number is good.


The number of poles is factor P. X/(0P). P=0 in this case. 0 poles means 0 weight is supported which means the hut has nothing to stand on. X/(0P)= X/(0*0), so dividing X by 0 means that there is nothing to support the weight.

Actually it's X/P, not X/(0*P) ( X/(0*P) will give the same result (error or 0, depending on the scenario) no matter the amount of poles). Which is the same as I just said, I simply already went with P=0.

By the way people, calling each other trolls is against the forum rules. Let's keep some amount of civility here.

[Decoy Lockbox]

This is really a riot. Its like the math equivalent of a teenager telling his dad "screw you and your rules old man!" before peeling out on a motorcycle.


The flaw is in bold. Zero will not go into the number, zero times; because zero will not go into the number at all. It's the same thing as asking how many times zero will go into banana. The answer isn't zero, it's the null set.

I assumed the answer had something to do with the difference between zero and null. Before I read your reply, I was going to post something like "the result of dividing by zero isn't zero, its null, like in computer programming".

[Zeb The Troll]

So basically it's the square root of -64, and don't nobody tell me that that = -8i without defining i.Very well. i is defined as the square root of -1. This is high school math, not even high level high school math. This is "middle of hick country 'how does this help me farm again?'" math. This is at a school where the Spanish teacher pronounced "Como te llamas" as "cow mow tea lamb oz" and nobody knew enough to correct her.

(And before you ask me how I can trust it, it's because that was the second time I'd had to take those classes. I'd taken them in junior high in Colorado before my family moved to Backwater where they didn't offer higher math but I still needed to have math credits in order to graduate.)

Also, for my clarification, because I'm seeing this pop up and I recall it being wrong, "divide by Zero" does NOT equal "infinity". It is "undefined", right?

[Quincunx]

So he refuses to use logic unless its his logic, and reverts to passive aggressive flaming ("your post is bs" and we all know what bs means) when proven unequivocably wrong.

Don't feed the math troll, guys. . .

Aw c'mon, I've got 5 bucks for the first person who pops FDM's much-vaunted* intelligence-cherry and teaches him to read mathematical logic, or at least teaches him that zero is a placeholder not a quantity!

*by himself, on this forum

[Yoren]

Just out of curiosity what level of math is "Math 94"? Geometry? Trig? Algebra 1?



Also, for my clarification, because I'm seeing this pop up and I recall it being wrong, "divide by Zero" does NOT equal "infinity". It is "undefined", right?

If I remember correctly for 1/x the limit as x approaches 0 is infinite but at 0 the function is undefined.

[Myrmex]

When a math teacher tells you that certain operations can't be performed on a particular set, usually what they mean to say is "we don't cover that in this class."

[kamikasei]

Mathematics is made up of conventions. Division by zero (on the natural/real numbers, etc. etc.) is undefined because division is defined and the definition excludes division by zero. You could try to extend the definition of division to handle that case, but you'd have to work around a great many problems that have been identified by better mathematicians than any of us here. If you were to succeed, which I think has been pretty thoroughly shown to be impossible the last eleventy-dozen times someone tried, you wouldn't have proven your math teacher wrong, you'd have devised a slightly different form of mathematics.

Here (http://scienceblogs.com/goodmath/2006/12/nullity_the_nonsense_number_1.php) is a blog post by a mathematician about a guy a while back who claimed to have revolutionized mathematics and cured the common cold by defining division by zero. You may find it illuminating.

Actually, this (http://scienceblogs.com/goodmath/2008/10/infinity_is_not_a_number.php) post probably addresses the issue more usefully, though less directly.

[Totally Guy]

I think we have some kind of variant of this going on.

http://imgs.xkcd.com/comics/words_that_end_in_gry.png

We have some kind of "nothing, zero, and 0" all having totally different meanings and being used interchangeably.

[Khanderas]

Apologies if it already have been explained satisfactory.

10 / X is infinity when X is 0. Thats the problem that needs explaning why.

10 / 1 = 10
10 / 0.1 = 100
10 / 0.01 = 1000
10 / 0.001 = 10 000
(skipping a few steps)
10 / 10^-500 = 10^500

as the denominator gets smaller, we creep ever so closer to 0 and the result virtually runs higher and higher. There is no limit really to how close (in math) we can get to 0, and every time we get alittle bit closer to 0, the whole number grows... and grows faster every time too.

[Rettu Skcollob]

People actually

http://i33.tinypic.com/256scnk.jpg

ARGUE about this?!

Excuse me... I need to get outside, and I suggest many of you do the same.

[Cubey]

People actually ARGUE about this?!

http://mohel.dk/grafik/andet/Someone_Is_Wrong_On_The_Internet.jpg

[kamikasei]

Apologies if it already have been explained satisfactory.

10 / X is infinity when X is 0. Thats the problem that needs explaning why.

Yes, the limit of 1/x as x approaches zero is infinity (or rather, there is no limit). But 1/0 itself is undefined. (Note that if you're looking at the integers that the limit is positive infinity if approaching from the positive direction and negative if approaching from the negative direction, for one thing.) Division is defined in a way that excludes division by zero.

This is not a problem. There is nothing to solve. This may be confusing or counterintuitive but you're never going to resolve your confusion if your instinctive reaction is to assume that all the people knowledgable in the field are mad and/or lying because their conclusions seem strange to you.

[Rettu Skcollob]

http://mohel.dk/grafik/andet/Someone_Is_Wrong_On_The_Internet.jpg

As for X/0 = infinity, I'll leave it for others to criticise.



http://i35.tinypic.com/2yk1gjr.gif

Can't we all just get along and argue about something at least slightly less pointless...? I'll make cookies...

[Cubey]

Yes, the limit is infinity as X approaches zero. It means that both X and f(X) = 10/X approach 0 and infinity, respectively. But neither of them actually REACHES 0 or infinity.
So you can't say that 10 (or any other number)/0 = infinity. It is a very close approximation, but not the exact result. And you still can't divide by 0.

[potatocubed]

Right, so just because I calling out the standard logic I refuse to use it? The current logic presented is /0=infinite, yet the only reason I'm given is, "Because".
The "logic" I'm handed is nothing more than being told that's just the way it is, with no real why.

Alright, let's try it like this:

The whole of the physical universe is based on physics, which is based on maths. Although maths seems abstract and unconnected with reality - and some of the further-reach stuff is - there are plenty of mathematical principles that you can reach out and poke, establishing their truth through experimentation. Unsupported objects fall. Caesium dropped into water goes 'bang'. /0 = infinite (or undefined).

Try this actual, physical experiment: make a pile of twelve jellybeans (or apples, or peanuts, or some other 'quantity' food). The number of trips it will take you to move that pile into another room varies depending on how many jellybeans you carry at a time.

If you carry all twelve at once it will take one trip. (12/12 = 1)

If you carry six at a time it will take two trips. (12/6 = 2)

If you carry three at a time it will take four trips. (12/3 = 4)

If you carry zero at a time, how many trips will it take?

By your maths, it will take zero trips; the jellybeans will magically ping into the other room. If you try this experiment at home, you'll find that this doesn't happen. Therefore, your maths is empirically proven to be false.

The answer is either an infinite number, since you can wander empty-handed from one room to another until the end of time and those jellybeans won't move, or an undefined number, since the whole exercise becomes pointless and you might as well just eat the damn jellybeans.

[Cubey]

Can't we all just get along and argue about something at least slightly less pointless...? I'll make cookies...

I'm sorry, but I can't help it. The original post just hurts me. And when proved wrong, FDM instead ignores the arguments and calls them bullcrap.

[Rettu Skcollob]

I'm sorry, but I can't help it. The original post just hurts me. And when proved wrong, FDM instead ignores the arguments and calls them bullcrap.


Situation 1)

http://i38.tinypic.com/3447adj.jpg
Lol i trol u

Situation 2)

http://i37.tinypic.com/2wf7iox.jpg
Lol im so smrt every1 else is wrong

In the end, does it really matter?

[Khanderas]

Originally Posted by Tengu_temp
Let's say we make a hut on poles, and somehow we devise it without any poles. The hut weights X, a single pole can only support Y weight before breaking. How much weight each pole is holding?

Scenario 1: normal math. Each pole is supporting X/0 weight, which means... oops, impossible, back to the drawing board!
Scenario 2: your math. Each pole is supporting X/0 weight, which means 0, which means the plan is fine because 0 < Y. Proceed with construction!
No, my scenario still states that each pole will support zero weight, as they aren't existent. The number of poles is factor P. X/(0P). P=0 in this case. 0 poles means 0 weight is supported which means the hut has nothing to stand on. X/(0P)= X/(0*0), so dividing X by 0 means that there is nothing to support the weight.

Ooh ooh... Let me try this version. :smallsmile:

I have a motorbike. In the tank I have X amount of gas. The engine "cost" Y units of gas per mile. How long can I drive without refueling ?

X / Y = Z

A normal number just to check for silly mistakes. 100 units of fuel. Every mile costs 10 units.

100/10 = 10 .. So I can go 10 miles, it adds up.
100 / 100 = 1 ... if I got 100 units of gas and it costs 100 units to drive one mile... I reach one mile.

Now. If my motorbike was magical and consumed 0 fuel per mile. how long can I go without the tank going empty ? Logically that would be forever.
The OP would claim that it would be zero.

So... 100 / 0 = Infinity (he never stops the bike, so it never reaches a number, thereby infinity, and evergrowing. It also doesnt matter how much fuel there are, for it is always there when the cost is 0)

[kamikasei]

Note that for a bunch of practical applications you can, in fact, say that dividing by zero yields an infinite result - the example Khanderas uses is such an application. But you can't do this in the actual math. You cannot prove anything about a formal system like math by analogy or real-world example - those can only help clarify formal statements - and if you try to say that the result of dividing by zero is formally infinity or anything else then you create problems.

[Khanderas]

Note that for a bunch of practical applications you can, in fact, say that dividing by zero yields an infinite result - the example Khanderas uses is such an application. But you can't do this in the actual math. You cannot prove anything about a formal system like math by analogy or real-world example - those can only help clarify formal statements - and if you try to say that the result of dividing by zero is formally infinity or anything else then you create problems.
Thats why my bike is magical :smallbiggrin:

It is true what you say though, my illustration was mainly to show why it shouldnt be defined as 0.

[Rettu Skcollob]

Thats why my bike is magical :smallbiggrin:

I have a sudden urge to bring up Inkscape and draw Khanderas driving away from this thread on a sparkly Harley Davidson, into the sky.

[Thufir]

OK, I think everyone who has entered this argument other than the OP has presented entirely valid, nay conclusive arguments as to why he's wrong... but I'm going to do it again anyway. Starting from his original post:


Let's take what we know first and foremost about division. Division is two things, it's repeated subtraction, and it is multiplication reversed. And these statements are truth. To multiply anything by zero, gets a result of zero. To subtract zero from anything, get a result of the original numerals.
So why does dividing by zero get an undefined result? The simple answer is that a number cannot go into zero. So then how does that make it undefined?

So yes, let's consider division first as repeated subtraction. To be more precise, division A/B=C indicates that B can be subtracted from A a total of C times before reaching 0.
So if B=0, A=/=0, how many times can it be subtracted from A before reaching 0? The answer is not 0. If you subtract 0 from A 0 times, you get A, not 0. Of course, this is true no matter how many times you subtract 0. So in fact, there is no defined number C such that A-0xC=0, => there is no defined number C s.t. A/0=C => A/0 is undefined.

Alternatively, as you say, division is the opposite of multiplication. I'll requote a little bit:

So why does dividing by zero get an undefined result? The simple answer is that a number cannot go into zero.
This is incorrect. You have the division the wrong way round. Trying to make a number go into 0 is 0/A=0. A/0 is trying to make 0 go into a number, a rather significant difference.
So, division as the opposite of multiplication. A/B=C => A=B*C. Now let B=0.
A/0=C => A=0*C=0. So A/0 only has a solution if A=0. So for A=/=0, A/0 is undefined.
(Also note that for A=0, 0/0=C and there is no way by this method that you can more accurately determine what C is. It could be anything)

[Khanderas]

I have a sudden urge to bring up Inkscape and draw Khanderas driving away from this thread on a sparkly Harley Davidson, into the sky.
Sounds awsome.:smallcool:

[Quincunx]

I'm thankful to all of you and your various proofs about zero and what you can and can't do with it; they span many levels of mathematical knowledge so we readers can jump in at the level we can handle.

(escorts the "magical pinging jellybeans" discussion to the thread about the Higgs boson, where the jellybeans can ping and spin in sync while we work out how momentum happens without mass) (Ping?) (Pong.)

[Rettu Skcollob]

Sounds awsome.:smallcool:

Sadly it is also getting quite late, and I have to get up fairly early tomorrow. :C But I'll get it finished one day, you'll see.

[Tirian]

It's of the same variety more or less, yes.

I can't think of any specific examples, but I have no doubt that there are definitely places where it is very important that /0 = infinity, NOT 0.

It depends upon which specific branch of math you're talking about. (Perhaps it is bothersome that the rules are different for different branches, but that's unfortunately the way it is.)

If you are dealing with complex analysis in the Riemann sphere (which, for the uninitiated, is the complex plane projected around a sphere with the origin at the "south pole" and an extra point called ∞ added at the "north pole"), then the function f(x) = 1/x maps every point to its antipode and in this context it makes some sense to say 1/0 = ∞ and 1/∞ = 0. (But it still doesn't make sense to say that 0*∞ = 1.) In pre-calc, you can sort of casually define the extended real numbers to be the numbers plus {∞, -∞} and define them to be the limits of all sequences that grow without bound

But that doesn't make ∞ a concept that you can pack up and plug in to other branches of mathematics. The real numbers have both algebraic and topological rules that need to be satisfied, and there is no consistent means of getting ∞ to satisfy all of the algebraic rules. It

Unless you're in the "here be dragons" parts of math, the definition of division really is reverse multiplication. To be precise, a/b is defined to be the unique solution x to the problem bx = a, and is not defined if that problem either has no solution (like 1/0) or more than one (like 0/0). I'm all for challenging the conventional, because there really really is a lot of math that deserves to be challenged, but you've got to show that your new definition solves more problems than it creates before anyone will adopt it, and I think that the proposal that 1645/0 = 0 has yet to clear that hurdle.

[bluewind95]

Ahh. The reason it is simultaneously the numerator, is because when you attempt to exert a non-effective force(in this case, your flat bucket, or "0") upon the pool(the numerator), the pool still exists.

Ergo:

0/0=1 or 0 or infinity.
X/0=X, 0, or infinity.

0 is both all powerful, yet null. Sort of a black hole thing. To explain more would involve possibly religious connotations.

Ahhh, okay. Yeah, this makes sense to me, I think. Division by 0 is all that, hence why it can only be considered to be undefined, yes?

[PirateMonk]

Like today I learned that the square root of -64 is not a real number, yet my friend learned in his super math that it in fact is. That's just a higher math. The rules are different, but the result wills till be the same.

Strictly speaking, the square root of -64 is not a real number. It is an imaginary number.

A physics explanation:
If something travels zero meters (or whatever) in zero seconds, its velocity is 0/0. However, it does not follow that its velocity is zero. It could be zero, but it could also be any other number, as nothing with a finite velocity will move in zero time, regardless of how fast it's moving. It is impossible to determine anything.
If it travels, say, 3 meters in zero seconds, then it travel infinite distance if it continued forever at the same velocity. However, it would do so in zero seconds, so its velocity could be infinite, or it could be undefined, depending on your definitions.

[RS14]

Ahh. The reason it is simultaneously the numerator, is because when you attempt to exert a non-effective force(in this case, your flat bucket, or "0") upon the pool(the numerator), the pool still exists.

Ergo:

0/0=1 or 0 or infinity.
X/0=X, 0, or infinity.

0 is both all powerful, yet null. Sort of a black hole thing. To explain more would involve possibly religious connotations.

X/0=X would imply that X=0*X. X/0=0 would imply that X=0*0. As others have said, it is somewhat reasonable to think of it as (plus or minus) infinity. But as this is not an element of the real numbers, therefor we do not actually define it in this manner.

[AtomicKitKat]

My point is that division by zero is generally an abstract concept. Most schools/teachers simply tell you "Impossible". What they really mean is "It could take 5 minutes, or 5 lifetimes to grasp it. I'd rather not bother." I "figured" it out when I was about 10 or so, because I just sat down one day, stared up into the sun, and let my brain wander. It's really not that hard to understand it, and after finding out about the whole Heisenburg's Uncertainty Principle(where a particle is in more than 1 place simultaneously, or something like that), it actually "makes (even more) sense" to me now. If you could actually bring it into a real world application, it would be like a Perpetual Motion Device, or the Infinite Energy Source.

[Telonius]

Sadly it is also getting quite late, and I have to get up fairly early tomorrow. :C But I'll get it finished one day, you'll see.

Might end up something like this (http://www.xkcd.com/622/).

http://imgs.xkcd.com/comics/haiku_proof.png

More relevant to this situation...

http://imgs.xkcd.com/comics/useless.jpg

We know that in tennis, love is zero. So clearly there are a wide range of problems that zero totally messes up.

[kamikasei]

My point is that division by zero is generally an abstract concept. Most schools/teachers simply tell you "Impossible". What they really mean is "It could take 5 minutes, or 5 lifetimes to grasp it. I'd rather not bother."

No. That's not what they mean. They mean that for division as defined over the naturals, integers, or reals, zero is not a valid divisor. It is impossible to divide by zero because it's a meaningless operation and the result isn't a number.

[Fiendish_Dire_Moose]

Just out of curiosity what level of math is "Math 94"? Geometry? Trig? Algebra 1?



If I remember correctly for 1/x the limit as x approaches 0 is infinite but at 0 the function is undefined.

Math 94 is Algebra 1.

So, yeah, I passed high school, never learned what i is and what not. So, saying it's high school math, isn't exactly constructive since apparently, it's not..

[RS14]

Math 94 is Algebra 1.

So, yeah, I passed high school, never learned what i is and what not. So, saying it's high school math, isn't exactly constructive since apparently, it's not..

Depends on where you are, then. Regardless, wikipedia's article on Complex Numbers (http://en.wikipedia.org/wiki/Complex_numbers), particularly sections 1.1 and 1.3, should be informative. See also Imaginary Unit (http://en.wikipedia.org/wiki/Imaginary_unit) for more detail on the properties of i.

[Fiendish_Dire_Moose]

Depends on where you are, then. Regardless, wikipedia's article on Complex Numbers (http://en.wikipedia.org/wiki/Complex_numbers), particularly sections 1.1 and 1.3, should be informative. See also Imaginary Unit (http://en.wikipedia.org/wiki/Imaginary_unit) for more detail on the properties of i.

Well, thanks for that, but I'm officially done here.

The point of this was to get people thinking about what we tend to think is right, even if it's troubling in the sense it makes.
It wasn't about being right or wrong, I said it too many times.
But like the current trend goes, nobody came in here to have any form of enlightening discussion, they all just came here to go, "No, you're wrong lol." And when I said it wasn't about being right, it was about thinking outside of the boxes we're told to, everyone just repeated themselves and called me stupid.
So, congratulations, as you all flock to tell me I'm wrong about something that wasn't about right or wrong, you all miss the entire point and teach me that you're boring people. You didn't want some conversation about the norm and its limits, you just wanted to be right.

So, thanks, thanks for ruining what could have been a fun brain storm for everyone.

[Cobra_Ikari]

Well, thanks for that, but I'm officially done here.

The point of this was to get people thinking about what we tend to think is right, even if it's troubling in the sense it makes.
It wasn't about being right or wrong, I said it too many times.
But like the current trend goes, nobody came in here to have any form of enlightening discussion, they all just came here to go, "No, you're wrong lol." And when I said it wasn't about being right, it was about thinking outside of the boxes we're told to, everyone just repeated themselves and called me stupid.
So, congratulations, as you all flock to tell me I'm wrong about something that wasn't about right or wrong, you all miss the entire point and teach me that you're boring people. You didn't want some conversation about the norm and its limits, you just wanted to be right.

So, thanks, thanks for ruining what could have been a fun brain storm for everyone.

But see, there is a field where there is no right or wrong. It's called "philosophy". Interjecting a nonsensical counter-answer to an established "right" in a scientific field...of course people will tell you you're wrong. You ARE wrong. Even if they're wrong too...you still ARE wrong. There can be more than one wrong, I guess.

Question all you want, but don't offer nonsense and tell people you're right. That's just being ridiculous.

[Fiendish_Dire_Moose]

But see, there is a field where there is no right or wrong. It's called "philosophy". Interjecting a nonsensical counter-answer to an established "right" in a scientific field...of course people will tell you you're wrong. You ARE wrong. Even if they're wrong too...you still ARE wrong. There can be more than one wrong, I guess.

Question all you want, but don't offer nonsense and tell people you're right. That's just being ridiculous.

I never told people I'm right, I never said I was right. I don't know why you people seem to think I do. I know very well I'm wrong. But. That. Was. All. Beside. The. Point.

I presented the thread as a contrary yet un-serious solution to a long standing undefined. And that's all.

[Shadowcaller]

I never told people I'm right, I never said I was right. I don't know why you people seem to think I do. I know very well I'm wrong. But. That. Was. All. Beside. The. Point.

So, if I said, 2+2=5, would that be a fun brain storming activity for everyone? I don't really see it, if you had used mortality or something, that would have been a discussion, but you use a exact science...

[Pyrian]

More relevant to this situation...

http://imgs.xkcd.com/comics/useless.jpgI have that T-shirt. :smallbiggrin:

[Gullara]

So, if I said, 2+2=5, would that be a fun brain storming activity for everyone? I don't really see it, if you had used mortality or something, that would have been a discussion, but you use a exact science...

Let it go he made an interesting point and although it wasn't "right" that wasn't the point, think outside the box people, jeez. :smallannoyed:

[Cobra_Ikari]

I never told people I'm right, I never said I was right. I don't know why you people seem to think I do. I know very well I'm wrong. But. That. Was. All. Beside. The. Point.

I presented the thread as a contrary yet un-serious solution to a long standing undefined. And that's all.

Does the following look familiar?


(I'm in math 94, so this may not apply to those of you more math savvy.)

Math, the single universal truth in the world. We made it, and we applied it, and guess what, it worked. It was provable, understandable, and teachable. But as time went by, it became more complex. As technology grew we found ourselves needing math more and more.
What started out as 2+2=4, became 2x+4(3x-2)=x7-(34-x). And it didn't stop there. Math gave us science, and science served to further our technology even greater. But in this single great universal truth there is the single greatest lie teachers tell their students. This lie of course, is that dividing by zero, is undefined.
Let's take what we know first and foremost about division. Division is two things, it's repeated subtraction, and it is multiplication reversed. And these statements are truth. To multiply anything by zero, gets a result of zero. To subtract zero from anything, get a result of the original numerals.
So why does dividing by zero get an undefined result? The simple answer is that a number cannot go into zero. So then how does that make it undefined?

Zero=nothing. No capacity to hold numbers, no capacity to go into a number. So if we take what we know about zero, and divide a number into it, shouldn't the result simply be zero? Of course it should.
How many times can nothing go into 1,645? None. Zero will go into this number, zero times.
How many times can 45 go into nothing? None. A number multiplied by zero, is zero, so dividing the same number by said nothing, is nothing. You cannot fit 45 oranges into a cylinder if it is unable to hold anything.
So, ladies and gentlemen, the next time your math teacher tells you that dividing by zero is undefined, challenge him/her, and call them out for their lies. And when you do, quote Big Boss with, "All things return to Zero."

I hope so. Now, do you realize how this comes off sounding? I'll explain.

"Hi! I'm not in any really advanced math, but this concept, which actually makes a lot of sense if you go into it? It's a lie perpetuated by math teachers. The correct answer is this nonsense I'm spouting here. Here, I'll even throw in some pleasant looking, but not quite logically sound, arguments for this. Now go tell your teacher they're wrong."

That doesn't sound like "I think this is wrong, and would like to discuss it." That sounds like "You are all wrong, I am right, here is my proof, now go correct people who actually know WTF they're talking about, kthanks."

It IS a bit offensive, I suppose. To then claim that you never meant you were right...sounds more like a cop-out to avoid admitting you were wrong than the truth.


It'd be like if I claimed the earth orbits the sun because we have a giant leash attatched, and to tell my teachers that they were lying to everyone and full of crap. And then when people were like "No, no leash, look, SCIENCE!", I responded with "I never meant the leash was right! Your science is wrong! I want logical discussion! You guys are all arrogant jerks who need to be right! Way to miss the point!"

I'm exaggerating, of course, but realize how your argument sounds before you make it. >.>

[Douglas]

Well, thanks for that, but I'm officially done here.

The point of this was to get people thinking about what we tend to think is right, even if it's troubling in the sense it makes.
It wasn't about being right or wrong, I said it too many times.
But like the current trend goes, nobody came in here to have any form of enlightening discussion, they all just came here to go, "No, you're wrong lol." And when I said it wasn't about being right, it was about thinking outside of the boxes we're told to, everyone just repeated themselves and called me stupid.
So, congratulations, as you all flock to tell me I'm wrong about something that wasn't about right or wrong, you all miss the entire point and teach me that you're boring people. You didn't want some conversation about the norm and its limits, you just wanted to be right.

So, thanks, thanks for ruining what could have been a fun brain storm for everyone.
If that's really what you wanted to do, math was absolutely the wrong subject to do it with. Math is one of those subjects where there most definitely are objective absolute rights and wrongs that just plain aren't subject to debate. There simply is no such thing as "thinking outside the box" in math unless you're talking about proofs of very advanced and complicated ideas, and then it's all about how you go about trying to prove something or, possibly, really strange things to try to prove that no one's ever thought about before. To get to a point where what you say you were trying to talk about is even valid at all in math, you have to be dealing with stuff that has not already been solved. Division by 0 is ancient news. There's one right way to handle it and that's it.

If you really want to start that kind of thread, either stay away from math and any hard sciences or make sure the particular problem you talk about is one that is not conclusively solved yet.

[kamikasei]

I never told people I'm right, I never said I was right. I don't know why you people seem to think I do. I know very well I'm wrong. But. That. Was. All. Beside. The. Point.

In general, when people advance a position, we assume they think they're right about it or at least are interested in hearing the arguments against it (if perhaps they're uncertain about it and testing its merits). It's sort of an assumption of good faith. If you can't assume good faith - if you have an expectation that people are just posting nonsense for the sake of it - then there's no discussion to be had. So I don't know what result you expected; either people were going to decide you were saying things you knew were incorrect simply for the sake of saying them, in which case there would be no reason to speak to you, or they would assume you thought you were right and had the intellectual honesty to withstand arguments against your position, in which case you'd get the thread that developed. How did you imagine a useful discussion would develop if people recognized your insincerity?


Let it go he made an interesting point and although it wasn't "right" that wasn't the point, think outside the box people, jeez. :smallannoyed:

...But he didn't. It wasn't interesting, it was simply wrong. What's the box we're supposed to be thinking outside of, here?

No, really, I want to know: what was the interesting point you feel he made?

[RS14]

It wasn't about being right or wrong, I said it too many times.
But like the current trend goes, nobody came in here to have any form of enlightening discussion, they all just came here to go, "No, you're wrong lol." And when I said it wasn't about being right, it was about thinking outside of the boxes we're told to, everyone just repeated themselves and called me stupid.

Well, I never meant to call you stupid. There is nothing wrong with considering alternatives in math. The problem is that defining division by 0 seems to raise more problems than it solves.

If you want to discuss math in any manner, we need some logical foundation on which to build proof upon which we can agree. Trying to argue with these default assumptions is something that should be done initially, before attempting to construct anything from these modified assumptions.

Now there are valid reasons to consider restricting our forms of proof. I'm familiar only with Mathematical Constructivism. But again, we do so in a rigorous way.

[Thufir]

Yeah, thinking outside the box is useful in high-level maths, but if you challenge a long established principle, you better have a good, logical argument to prove why you're right and everyone before you was wrong. Even then, people will likely do their best to tear your idea apart.

And just one point:

It wasn't about being right or wrong, I said it too many times.
But like the current trend goes, nobody came in here to have any form of enlightening discussion, they all just came here to go, "No, you're wrong lol." And when I said it wasn't about being right, it was about thinking outside of the boxes we're told to, everyone just repeated themselves and called me stupid.

Emphasis mine. I looked back through the thread. When you said it wasn't about being right, it was about thinking outside the boxes we're told to, was in fact, here. This was the first time you said it. The rest of the thread you just vehemently defended the idea you forwarded in the first post.

Now, if you'd instead used division by zero as an analogy for thinking about things differently, trying to do the impossible, etc, then maybe you would've got a decent discussion on that subject out of it.

[Roland St. Jude]

Sheriff of Moddingham: Thread locked for review.