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# why 0/0 is not define?

Note by Arvind Dangi
3 years, 8 months ago

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0/0 is not defined for two reasons: 1: you can easily find multiple functions which have different behaviours as we get closer to the point in which the dependent variable equals 0/0. Examples of such functions can be y = 1/x, y = x/x, y = 2(x-1)^2, and y= x^2/x. 2: Let's suppose 0/0 could be defined, and represent the possible definition with "a". That would lead us to a = 0/0, which could then be turned into 0a = 0. Doing that would give us absolutely no way to assign "a" a value, as any number (except infinity, as multiplying zero by infinity or minus infinity is undefined, but that's another story) you replace the variable with will satisfy the condition 0a == 0. Note that when you know that 0/0 is undefined, it also means that you can't multiply 0 by a/0 to undo the division by zero, nor divide 0a by 0 to undo the multiplication by zero. I only did that in the second reason because we assumed that there could be a way to define 0/0. We also can't divide a number by 0 without getting the result undefined, by the way. This is why we can't simplify something such as y = (x^2)/x into y = x.

Here are two links that may interest you and other readers: www.khanacademy.org ; www.mathsisfun.com · 2 years, 10 months ago