Raptor115

OK.... You've said it. I guess it all comes down to the value of 0*0. OK... I agree that you and tmpst have the best argument so far(BTW I WAS arguing for the sake of argument. Otherwise, why would I consider myself to be out of my own mind). In any case, I think it all comes down to this --- How do you say 0*0 = 0. OK this might seem like a stupid question, but really, I'm sincere in asking it, because ---- Let's consider: 2*3. In Maths, multiplication is adding the first number for the number of times given by the second number, right? So this is 2+2+2 = 6. We could write this as 3*2 --- 3+3 = 6. So we get the Commutative property and by further proof, the Associative property. Now for multiplication with 0. 6*2 means 6+6. 6 * 1 means 6. 6*0 means ___?(Nothing?. Oh, that's what zero is..., right? Wait.., we write 0 one time so its 0*1) Using commutative property we write 6*0 as 0*6 --- 0+0+0+0+0+0 = 0. Now, how do we define 0*0?? Please, I'm really serious. I'm not joking or making fun. The point is if we write a number once, it's that_number * 1. If we multiply 0 with 0. That is, 'Nothing' added 'nothing' times. What does that mean? There are?? Can you please point out and explain some of these systems.

LOL.... I thought I said I was giving the value of 0/0 and not 0. You yourself say 0/0 is not 0. Then how do you say 0 = 0/0 =1? To The Moderators: I'll be going away for a week, and to a place where there is no internet connection. So please don't close this thread. The debate's going nicely.

Exactly my point. If you take it as y =x, you'll have infinite solutions. Rewriting it, x - y = 0. Now add another equation, like x + y = 2. Then solving both you get x = y= 1. Now when I said 0/0 doesn't make sense in elementary arithmetic, I meant exactly what you mean --- It has infinite solutions. Now take some other functions like f(x) = x/x or 2x/x or -3x/x or 4- x2 / 2 - x. In all these equations, we can simplify to a form where we KNOW the answer like f(x) = 1 or 2 or -3 or 2+x. Now comparing all these.... if we take 0/0 = 1, we get the answer we're supposed to get when we simplify them. That's why I thought if we define 0/0 = 1, we could maybe simplify a few things, rather than contradict them. And that's what I've been saying all along in this article. Give me one contradiction with 0/0 = 1 which I can't solve and I'll give it up.

Sorry for that.... Really. I was a bit sleepy at that time (Well I can only switch on my comp after 8 pm, what with school and after-school tuition). The thing is..... I just thought I said that you can't define 0/0 with real-life examples in the original post and so I thought you hadn't read it fully. Like I said, if someone can define i = the square root of -1 with a real-life example, I'll say, that guy has real genius. OK..... lets see if me can twist this one...... OK Here goes, its like saying x = x.1 = x. (x/x) = x/x = 1? Where did the extra x go? Oh well..... if you take x as zero that might work out... but actually I thought of this for a long time and I saw in another website that they had an argument like if f(x) = x/x = 1 for x = 0 then f(x) = x2 /x = x = 0 for x = 0. Well lets see what you did. 0 = 0.1 (OK, its the same value) = 0 x 0/0 (Putting what I just said) = (0 x 0) / 0 (Well there ain't no bracket in the first place, so I'm gonna rewrite this as 0 x (0/0)). So we have 0 x (0/0) which is 0 x 1 (If 0/0 = 1) which is equal to 0. So 0 = 0. Nothing's changed right?? OK.... if you still don't understand we'll put it like x2 / x simplifies to x. Therefore, 0 x 0/0 is 0. I must say that it seems like I'm twisting the facts to prove my "hypothesis", but hey, I'm not like "I KNOW 0/0 is 1 and everybody else is a fool", I'm like "OK, if we say 0/0 = 1, then sure there are problems, but can't we solve those problems. I mean like, before the Indians came up with 0, the mathematicians must have struggled a lot with this concept of nothingness. Now I'm just trying to come up with something for 0/0, which doesn't cause contradictions. Now don't say there's a contradiction as soon as you say 0/0 = 1. I think we can solve the contradictions. Now, if someone presented me that 0/0 = 1 has a contradiction which would be unable to solve, I'll give it up. LOL, you must have spent a month dreaming about it for sure. Well.... if I was to say this at school, the Maths teachers would come at me with a slipper in their hand.... Its hard not to lose a doubt. I had an idea about producing unlimited electricity by placing motors and generators on the same axle, but everybody said it wouldn't work cause there'd always be some kind of loss... and I gave up on it.... Well that's a topic for the physics forums and not for maths so don't ask about it in this thread. Oh and please remember.... 0 is not equal to 1. Neither did I say x/0 = 1. I was only thinking about 0/0 and NOT about 0 or x/0.

OK, but why? I actually meant how do you equate co-efficients of x2 of two equations when x is not zero. Am I ignorant of any intermediate steps in such a procedure. I know well enough the intermediate steps in equating ax = bx LOL.

SIGH......... I tell it and tell it and tell it......... Please read the original post and all the replies. This is purely a hypothetical question which has no real answer. Its like asking to define i = square root of -1 with a real life example. I have seen this same viewpoint in many other websites. Please... before replying read my original post fully, read all the replies and post something new.

OK I'll admit you stopped me in my tracks for a minute there. Then I got a curious kind of doubt. You know when you have two equations like ax2 + bx + c and fx2 + gx + h and when they're both equal, we have this "equating co-efficients of x2" and "equating co-efficients of x" stuff. How do you say they equate coefficients without dividing anything? Am I ignorant of any intermediate steps. I'm only 15 so I'm not that expert in Maths, but I can hold my own.

OK, maybe I'm ignorant, or maybe its just my mind. 0/0 doesn't make sense naturally. I concede. Then tell me how i = square root of -1 makes sense naturally. Probably you didn't read all my replies. I did demonstrate that Maths is broken if you consider equating with "multiply by zero" operations. Consider two equations ax + c and bx +c. We know that if ax + c = bx + c, then a = b. Lets try putting a few values. x = 3; c = 1; so we get 3a + 1 and 3b + 1. If we get 3a + 1 = 3b + 1, then a = b right? OK lets put different values. x = 0(GASP!!); a = 1; b =2; c =3. We get (1x0) + 3 and (2x0) + 3 => 0 + 3 and 0 + 3 => 3 and 3. Since 3 =3 we say a=b and we get 1 = 2. See, I neither divided by zero nor did I assume the solution of x2 = 1 is one (What does that have to do with 0/0??) I think I proved Maths has contradictions without assigning a particular value to 0/0. Thanks. I just happen to be good at written English. When it comes to spoken English................ Again, I think I just proved that Maths is already unstable with "multiplication with zero" as it is with "division by zero". Maybe the solution is to say multiplication and division operations with 0 are indeterminate??

Not quite right on that point. I don't see 0/0 being ∞ anywhere. Its basically indeterminate LOL that's a good definition actually. Just kidding..... Don't take this seriously. Is this a joke?? OK lemme see Pi is exactly what you get when you cut the magic number 'e' off a "pie". Bah, doesn't anyone ever read my first post fully? I've repeated it like 5 times ---- 0/0 doesn't make sense in elementary arithmetic. So don't use real life examples. Maybe if you can demonstrate the value of i in i2 = -1 with real-life examples, then I'll accept that 0/0 is NEVER 1 in any circumstance I demonstrated that Maths is broken without even saying 0/0 = 1 in a previous reply. So I disagree. On the other hand you've taken (1x0)/0 = (2x0)/0. Well let's put it in a different way. We are going to take 0/0 = 1. Then, 1x0 = 0; 2x0 = 0. The whole thing becomes 0/0 = 0/0; 1=1. Maths is not broken by saying 0/0 =1. Its already broken if you consider my ax + c = bx +c example. OK. I'll change that to "hypothesis". Besides I didn't drink tequila, I drank too much coffee last week.... couldn't sleep much...... Just kidding. First off, I didn't pick that function out of the clear blue sky, I picked it from my sky-blue Mathematics Textbook Volume - 2 (The first volume is orange-orange). Well there ain't a difficulty about f(x) = 2x/x which is f(x) = 2 and f(x) = -3x/x which is f(x) = -3. If 0/0 = 1, it would satisfy all the conditions whereas if 0/0 = something else it would not. How? you ask? OK lets see; f(x) = 2x/x. Then, f(0) = 2 x 0/0 = 2 x1 = 2, which gives us the right answer. Same method to prove f(0) in -3x/x would give -3. If you'd started this hypothesis with 0/0 = 2 ( or 3 or 4 or -10) then you wouldn't be getting 2 x 0/0 = 2 x 1 = 2. you would get 2 x0/0 = 2x2 = 4 ( or 6 or 8 or -20). Next, if 0/0 = 1, then 0 - (0x1) must be 0, right? Oh well, lets see; 0x1 = 0; Therefore 0 - 0; That's 0, right? So what's wrong? Well, you're wrong about assigning 0/0 opening the mathematical door of death. I already pointed out we could prove 1=2 without needing 0/0 to be 1. If you really believe assigning 0/0 opens the mathematical door of death, please explain more clearly. OK, till now, except for D H, everybody posted why 0/0 isn't 1. I'm not asking why it isn't. I'm only asking why it shouldn't be 1. If you can't understand the difference between those statements, the first one's like saying "why aren't we cloning humans?" The second one's like "what's gonna be the problem if we clone humans?" Also, if you find my English difficult to understand, I'm sorry, I'm an Indian.

LOL that's a nice one. OK consider --- The pie's in your stomach. How many pies have you in your hand --- 0. The stomach divides the pie into infinite (well, to be precise its as many atoms as were in the pie originally added with the atoms in the saliva and digestive juices that went with it) pieces using HCl. How many pies does it leave in your hand --- 0. Division happens...... OK that was a joke. Basically that's exactly what I told in my first post. I mean, please read my post carefully once and you'll find that I SAID that 0/0 DOESN'T make sense in elementary arithmetic. I only said that in relation to the function f(x) = x/x. Its like a theoretical question. Like we know i2 = -1. We all know there ain't a real number like that. Yet we still don't disown it. Maybe my question comes along these lines. i'm sorry for writing this para and I'll edit n' remove this tomorrow. But for Greg, sorry but i gtg sleep. Its 11.45 pm and I have to go school tomorrow and work with my friend on the trinomial theorem (a+b+c)n . We don't know if it's already been done, but we certainly want to do it ourselves without external help. We got our models right today and we need to come up with a gen. formula by this week. Keep the arguments coming --- and please include a bit of humour. That way, the debate won't be dry. Good luck at some other arguments Greg.

@Greg I just re-read your first post and I realized I missed a big chunk of what you were trying to say. Also, I thought that you hadn't (I don't want to sound rude) read my post fully at first. I just told at the starting that 0/0 was and is meaningless (I don't know about "will be"). I was saying that f(x) = x/x could be simplified to f(x) = 1 and therefore f(0) is 1. You just took it as f(0) = 0/0 and said it would make a point of (0, y-axis(more specifically -infinity to +infinity)). OK that's like saying f(x) = x2 - 1/ x- 1 gives (1, y-axis) when x = 1, when it gives (1,2) when simplified. I'm applying the same simplifying concept to f(x) = x/x to say f(0) = 1. Umm... about your saying "it just doesn't help us in any way"..... I just realised its true. But it still doesn't convince my crazy half that this debate's a waste

@Joatmon LOL you got the point wrong. Actually by the f(x) = x2-1/ x-1 example, I wasn't trying to equate 0/0 with something. I thought I said it was meaningless to equate 0/0 with anything. OK if i didn't I'll say it at the end of this reply. Actually I meant that, like we could simplify f(x) to give x+1, we could also simplify f(x) = x/x to f(x) = 1, which makes even f(0) to be 1. @Greg you said X x 0 =0. Basically, we know that if ax + c = bx + c, then a = b. then putting x= 0, a =1 , b =2, c= 3 we get 1x0 + 3= 2x0 + 3 => 3 =3 implying 1= 2. @Joatmon, like this we could equate 0 to all the numbers known. (Agreed, I AM twisting the facts now) All I'm saying is that, saying 0/0 = 1 doesn't change things that radically, cause you see we can prove 1 = 2 without proving 0/0 = 1. Besides I wasn't doing a graph of "Find x such that x x 0 = 0." I said it was f(x) = x/x. OK, now for the divide-multiply headache. 0/0 = 1; 1 x 0 = 0; Finished. No violation of the law. If you think I missed any of your points please point it out. Also I do know 0/0 is meaningless in elementary arithmetic. As I said I probably was out of my mind last week and I couldnt rest till I started a debate. BTW I didn't think there would be 2 responses in 15 mins (Responsive website this. Some websites you don't get replies for weeks.....) Also, keep the arguments coming. I'm not going to stop till I find one that'll overload my brain. (Meaning it can convince my crazy half that this debate's a waste)

Hi, I'm Raptor(I'm not allowed to use my real name on the net as I'm only 15 now). I just joined to start a debate. You can find my post here

OK I admit I thought I was losing my sanity when I thought of this, but then I realized people thought Galileo was crazy when he said that the Earth went around the Sun. I am a (fairly)good mathematician and I know better than to question integer division by zero is undefined, but what about 0/0. Basically, for the past one week I was thinking about 0/0. Not integer division by zero but only about zero divided by zero. To prevent "You must be out of your mind" replies, I would like to state the.... uh.... rules first. Here's my theory. f(x) = x/x is a constant function giving the value 1. Therefore, 0/0 is also 1. IF you're going "OMG, Gasp.... what a sacrilege!!" wait... I have googled this item and have seen the replies. None of them are... uh... convincing...(I don't know the exact word for that feeling). So here's the deal 1. This is only a discussion/debate. Not a correctly-verified-and-proven theory. 2. First, I get to twist the facts to suit my theory. You mathematicians are going to state a theory without twisting the facts to REALLY disprove my theory. 3. If you can't do that you're going to get the chance to twist the facts to disprove my theory. (I have no doubt that's going to be as easy as "pi") OK, before you start chewing my tail I'll admit a few things first. Granted, 0/0 IS undefined when taken in elementary maths. (Come on how can you divide "nothing" sweets among "nobody" persons, to quote the classic textbook example). But as a function. Like f(x) = x/x. Simplifying we get f(x) = 1; Which is a constant function; Meaning it IS 1 for all x belongs to R. Its like the other classic example for limits; f(x) = x2 - 1/ x-1 is not defined when x = 1. But we KNOW it IS 2 when x = 1; Simplifying f(x) = x2 - 1/ x - 1 gives f(x) = x + 1. I'm stating my case on this principle. Ok, let the waves of opposition begin! EDIT: Oops, I ought to have read the forum sticky before I posted this. Moderators can move this to the "Speculations" section if they want to.