no no no - it's perfectly rational!Think of it this way - division is just the short hand way of saying 'divide x things into y groups'. So, 6/2 = 3 is the same as saying that 'six objects in two groups means there will be three objects per group'. So, dividing by zero means that you put x items into ZERO GROUPS - no matter what you do, by the definition of a group, and the fact that you have things to put INTO groups, you can't divide by zero.Admittedly, the metaphor fails to hold under scrutiny, as you can divide by things other than integers. But it's a convenient lie to help illustrate something, no?Steph41 months ago#965reply

and now you understand.Steph41 months ago#966reply

Oh yeah, I understand.It's all bupkis. It's an operation and all operations have a result.If you divide n things into 0 groups, you get 0 things.*hammers foot*swb41 months ago#967reply

how so? Even without dividing the things in the first place, you've got one group - the one they're in.Yes, all operations have results. Not all operations have results for all values, though. log of 0 isn't defined, for example.Steph41 months ago#973reply

Actually... the divide by decimals can be thought of as X/Y = "how many groups would you have if you put X items into groups of Y. so 6/3, if you put 6 items into groups of 3, you have 2 groups. 4/.5, if you put 4 things into groups of .5, you have 8 groups of ".5". But how many groups would you have if you're splitting into groups of 0? still undefined.Dave41 months ago#977reply

Anything divided by zero is infinity! (except of course zero squared divided by zero - thats zero.Duke of New York - A-NUMBER-ONE!41 months ago#978reply

Thankyou Steph!I completely agree.SWB, you are a stubborn blaghard! Think of it like this, you have n objects to divide into 0 groups. Where do you put the first object? You have nowhere to put it, so you can't do it. Simple as that.If you do it by mathematical sequences, logically dividing by zero always gives infinity, as I see it. I'd have thought youd appreciate that answer more.Dylan40 months ago#981reply

@MathnutsA basic division operation needs 3 variables: the dividend, the divisor, and the quotient (the result).If one is consistent in how one divides, the [quotient] is always going to be the quantity in any group if you divide [dividend] evenly into [divisor] groups.If you divide anything evenly into 0 groups, each has a quantity of 0. You need at least one group to hold a quantity higher than 0.One day math will catch up with me. I'm sort of like a modern day mathematician of the past. Zero is a hard to concept to comprehend and not many minds have the raw horsepower to keep up with some of the conclusions I come to.swb40 months ago#982reply

@swbalright, fine. we'll assume that dividing n things into 0 groups, you get 0 things.Where do they go? If you approach zero slowly, it seems that you'd get a much larger number of things per group, progressively - 5/5 vs. 5/4 vs. 5/3 vs. 5/2 etc..., a pattern which continues into the decimals. So where does zero come from? Like the Duke of new york mentioned, if anything, you'd expect the number of things to approach infinity, not zero. Also, I resent being called a 'mathnut' just for pointing out something that (to me, at least) seems rational. Steph40 months ago#988reply

@StephActually, the pattern continues towards one with integers. Yes, the fewer groups you divide it into, the more will be in each group. Which is why some say the result is infinity with 0 groups (that you can divide it into 0 groups an infinite number of times). But I still think 0 makes the most sense as a default result - you can't return infinity.And I wasn't referring to you, I was referring to the mathnuts, of course.swb40 months ago#990reply

seth is right.Diving by zero doesn't return a result, because it's not a valid operation. As Steph said, an analogy with groups makes sense, and shows you that clearly. If you need more insight, visit the link below -- a clear and concise explanation by a mathematician.It's not about /what/ should division by zero return, it's about the fact, that it /can't/ return anything, because the operation itself doesn't make any sense.http://scienceblogs.com/goodmath/2008/12/zero_classic_repost.phpfet40 months ago#1002reply

another thingIf you have: x / y = zthen, for all values (except when y=0), this is also true: x = z * yBut, if x != 0, and y = 0, z * y also equals 0:z * y = 0so you're left with x = z * y = 0, which is not the case, because I started with x != 0.Stop hitting the wall and accept the fact that divison by zero doesn't make sense.fett40 months ago#1003reply

*crank*swb40 months ago#1004reply

Adding my two cents into this mix, dividing by zero is as bad as, if not worse than, saying that 0.999999999... (the 9 repeats endlessly) is not equal to 1:1/9 = 0.111111111...2/9 = 0.222222222......5/9 = 0.555555555......8/9 = 0.888888888...9/9 = 0.999999999...Wait, isn't n/n the same as 1? That means that 9/9 = 1. We just proved that 9/9 is 0.999999999... though. We must conclude that 0.999999999... = 1 as a result.There is another oddity in mathematics regarding the summation of an infinite series. Suppose you had 1. You divide that value by 2 to get 1/2 (0.5) and add it to the 1, resulting in 1.5. You divide 1/2 by 2 to get 1/4 (0.25) and add it to the 1.5 to get 1.75. You continue this for an infinite amount of time. Eventually you will reach the conclusion that the sum of the series is 2. However, that's impossible because the sum will never actually reach 2. It will just keep getting closer and closer and closer after every power of 1/2 is added.The idea of using tangible objects to represent this abstract concept is illogical though. While I applaud Steph's effort, I must decry her method. After all, how do you explain how to group 3 items into groups of -4 or perhaps you have -3 items in groups of 4 (-3/4)?Also, for those that believe anything divided by 0 is infinity, you are incorrect. x/0 when x != 0 is AN infinity. Infinity is not a number, it is a concept. You can get into Calculus and deal with them in a highly abstract, yet rational, manner or you can simply group all of the possible infinities together as a single entity known as "infinity". As for 0/0, technically we cannot conclude anything. After all, x*0=0, so what would be the quotient (the variable 'x' in the multiplication version)?Yes, I'm a maths nut (the noun is "mathematics", not "mathematic"). I'm proud of that fact. There are many ways to use one's brain, and being skilled in maths is just an example of one.Dustin40 months ago#1008reply

Lets resolve thisComments about Dustin’s reply1) Steve is a he, not a she.2) How do you group –3 items in groups of 4? Easy if you are going –3 feet/second (speed being vector based, therefore you are driving in reverse), and if their are 4 feet per unit, then you are going –3/4 units/second. This type of math is practical and used to solve Engineering problems.3) Mathematicians and Engineers treat infinity as a number, not simply a concept.4) He says, “If you have: x / y = z”....” But, if x != 0, and y = 0,” and then tried so make some point about division by zero “doesn’t make sense” which isn’t proved by his scenario. Say x=1, then z = infinity. Then 1=0*infinity (x=z*y). It is a rule that 0 times infinity creates an indeterminate answer, meaning it can be any number (the number exists, we just can’t tell what it is from the equation). This tells the engineer that he needs to create another equation in order to determine what X is. 5) A practical application can be found in physics: a photon has no mass, but it does have a measurable momentum. Momentum is (elementarily) defined as: P = m (mass) * v (velocity)When something reaches the speed of light, its mass is increased infinity. So the effective momentum of the photon is: P = (0 * infinity) * v.Of course, in this case, infinity can be reduced to any constant over zero, which changes the expression to:P = (0/0) * vIs that a problem? Not for the universe; photons have a definite and measurable momentum.Dividing by 0 does make sense!!!!!!!!A computer program should not return 0 if the divisor is 0. If it would, then many equations that physicists use (for example the P = m*v) would give wrong answers. An engineer needs to know when the answer is indeterminate, and not have the equation result in 0. Sometimes these equations get quite complicated, and the Engineer would not realize he is dividing by 0. If (x/0 + y*z) returned (0+y*z), the engineer would get a numerical result that he would believe to be accurate, when in reality it wasn’t a plausible situation.Why do computers return ERR?As programming languages progress, division by 0 will probably be allowed, and will return infinity (as Maple math software does). The reason why most computers return “ERR” is because (for speed purposes), they use binary arithmetic. In the ALU the algorithm with first subtract the divisor register from the remainder register and place the result in the remainder register. If the divisor register is 0, then the quotient register will be shifted to the left, setting the new rightmost bit to 1. Therefore the answer in binary will always be 1111111111..... (for as many times as the division algorithm is programmed to repeat). When 1111111111..... gets converted to decimal, it would result in 9999999.....(for as many significant digits as allowed by the calculator or program). This type of result could cause Engineers to believe they have a determinant number, when in reality they do not (we don’t need more of the Hubble telescope conversion screw ups), so the makers of ALU’s typically return “ERR” before attempting to run the algorithm.Philip40 months ago#1122reply

Am I the only person that found out 0 times infinity = 1 and 0/0 is one? I think everyone else is being dumb on purpose. It just makes all the math work. Like y=xsquared/x when x=0 would make math teachers cry but it's obviously 0 cause it's the same as y=x.And most obvious - calculas is basically founded on 0/0 equals one. Derivatives = limits without the limit.Anonymous39 months ago#1243reply

Well folks, there's only one logical way to solve this...VULCAN DEATH MATCH!NA NA NA NANA NAA NANA NAAAAA....InterestedSpectator39 months ago#1363reply

It's a mathematical thing, you wouldn't understand.Ben39 months ago#1365reply

Why you can't...The problem here is everyone's definition of "division"... You're not splitting things into groups, you're "undoing" multiplication. It's not possible to multiply by 0 and get a value other than 0. Therefore, it doesn't make sense to be able to divide a number by 0, unless that number is 0, and then you (arguably) have either 1, or 0. And then how to choose which of those in that one case? You can't."Dividing into groups" is an oversimplification of what's *really* happening. It's a simple way of looking at it when dealing with whole numbers, which is good enough to get someone through grade school. When you get into the full integer set, and then into rationals, reals, and imaginaries, the concept falls apart. You can't use the "divide into groups" concept anymore. Division is the inverse of the multiplication operation. It's that simple. Define multiplication for a number system, then division is the undoing of that operation.So... Because there's no system that x * 0 = y (where x and y are numbers, and may or may not be equal), division by 0 remains undefined, and must do so. As I said, even the special case of 0/0, both 0 and 1 are equally likely, so an answer cannot be derived.Felonius39 months ago#1499reply

Additional aside about InfinityWhich one? There's a few... Countable? (all positive integers...) Uncountable? (all numbers (real, irrational, whatever) between 0 and 1) Philosophical? Religious?Felonius39 months ago#1500reply

Umm, the metaphor of dividing into groups does not hold up unless you're in elementary school, talking about natural (counting) numbers. Think about dividing by fractions, it's like talking about digging half a hole.The best way to think of it is approaching 0, not 0 itself. When one divides a number by smaller and smaller numbers, the output approaches infinity or negative infinity, an asymptote on the graph--the lines approaching the asymptote never stop.That x/0=infinity (if x is a real number not 0) has to be accepted for its applications, like relativity in physics.Anonymous39 months ago#1519reply

can't believe I'm feeding the trolls...if the right limit and the left limit are not the same, then it's undefined. ignoring the limit notation, x/0 for positive zero is infinity. x/0 for negative zero is negative infinity. -0=+0, so we get two different results for the same question - hence, undefined.dg39 months ago#1547reply