+9657 I have been reading a book which states that 1/0 = infinity. But Melody said
'Any number divided by 0 is undefined.'
I am thinking that \(\frac{12}{0} = 12(\frac{1}{0})=12\infty=\infty\)
Which one is right? Book or reality?
+36917 12 /x as 'x' APPROACHES 0 the value APPROACHES infinity. Melody is correct....dividing by 0 is 'undefined' or not allowed.
+118608 Hi Max and ElectricPavlov 
Let's consider this problem for a moment....
Here is the graph of \(y=\frac{12}{x}\)
You can see tha as x approaches 0 from the positive side that y approaches +infinity
BUT
As x approaches 0 from the negative side then y approaches - infinty
This is why 12/ 0 is undefined ..... it cannot be negative infinity and positive infinity both at the same time ://
so
\(\displaystyle\lim_{x\rightarrow 0^+}\:\frac{12}{x}=+\infty\\~\\ \displaystyle\lim_{x\rightarrow 0^-}\:\frac{12}{x}=-\infty\\~\\\)
In arithmetic, the rule is that you are not allowed to divide by zero. The fraction 1/0 is undefined in the sense that the operation of dividing 1 by zero simply can't be carried out. You are not allowed to do it.
Compare that with the situation of asking what happens to the fraction 1/x in the limit as x tends to zero. Here you can say that as x gets smaller and smaller, (though not actually reaching zero), the value of the fraction gets bigger and bigger. It gets bigger without limit. Think of a number as big as you want and a value of x can be found so that the value of the fraction is bigger than your number, and the value of the fraction will be bigger than your number for all (non zero) values of x smaller than that. In this case we say that the limit is infinity, and write (inaccurately) that 1/0 = infinity.
