I got into a ......debate over this problem. I said the answer was not possible while he said the answer was 0. y = z - x/y where y=0, z=0. what is x? On top of that, would this be consider algebra or calculus or even pre-algebra?
It's 0. Multiply y to both sides of the equation, which gives you y^2 = yz - x. 0^2 = 0*0 - x 0 = 0 - x x = 0
Ok awesome! Question on that though. y = z - x/y 0 = 0 - x/0 0 * (0) = (0 - x/0) * 0 Dont you have to do the parenthesis first?
y= z - x/y if the question is to solve for x ... isolate it before putting in values y-z = -x/y y ( y-z) = -x 0 ( 0-0) =- x I think x should equal zero.
In this formula as presented, it is impossible to determine the value of x put the actual numbers in: 0 = 0 - x/0 ANY number divided by zero is zero. So, x could be any number at all Technically I guess you would call this algebra, but really it's just a silly math problem. Zero equals zero minus ( (X) divided into zero parts ). Unless you have the formula mis-typed somehow?
That's my thought. The only difference is that, my high school teacher said the result of any number divided by zero is 'infinite', not zero. One way or the other, this equation is unsolvable. There is no answer to it.
No, the formula is written as it was. I think the premise was supposed to be not being able to divide anything by zero, getting undefinable as a answer.
I agree with kevc's answer, but I would reason about it differently. Since y = 0 and z = 0, we know that x/y = 0. So, just solve for x: x / (0) = 0 If x is anything but 0, then x / (0) would be infinite (certainly not 0). So, by process of elimination, x must be 0. Note that if you just asked what is 0/0, we can't say for certain that the answer is 0. But, if you know that x/0 = 0, then x has to be 0. To put it another way, if you have: x / 0 = w Then x = 0 IF w = 0, but not vice versa.
And that's what I am trying to get at. Dividing by zero is not possible. x could be any number from negative infinity to infinity but as soon as it is being divided by zero it is supposed to become undefinable.
But does this not negate everything? You just we know that x/0=0 ANYTHING over 0 is undefinable meaning it does not hold an answer Even 0/0 is undefined.
Exactly, multiplying both sides of an equation by 0 is like flying a spaceship through a black hole. It will never be the same when you come out from it (if you can).
It depends. As long as X isn't 0 that it is undefined but if X is indeed 0 then you have a whole slew of problems since you have a 0/0 indeterminate problem. (If you have 0/0 it means several things. Let's say this. x/x is 1. while 0/x is o. finally x/0 in undefined. So in essence all those are probabilities that are possible unless you have the aid of a derivative or integral that can show otherwise.) It looks like you have a Parabloid though.
Perhaps I'm looking at it from an engineering/practical perspective rather than a theoretical one. My assumptions: - I'm interpreting "0" as an infinitesimal quantity (very small, approaching literally 0) - "Undefined", to me, means the problem isn't specified enough to settle on a unique solution for x. If the formula is 0/0 = x, then I would say x is truly undefined. If you take one infinitesimal quantity and divide it by another, there's no way to know what the result is (it could be huge or it could be really small; it could be positive or it could be negative). But if you give the formula x/0 = 0, then to me x is no longer undefined. It must be "0" (i.e. an infinitesimal quantity). That is, if you divide a quantity by an infinitesimal number and you get as a result an infinitesimal number, then the original quantity must itself also have been infinitesimal. With your original formula, if instead of saying z = 0 and y = 0, you said that z and y were approaching 0 as a limit, then x is defined -- it is also approaching 0 as a limit.
dividing anything by 0 is undefined just like the function f(x)=x^2/x is undefined when x=0 despite simplifying it to f(x)=x.
This. It completely depends on your level of Math. In most cases, any integer divided by 0 is undefined. However, in some branches (Limits, e.g), then 0/0 creates a whole array of possible solutions. Or I can be completely wrong, and it's 0. Who knows. Is this Algebra?
