When we calculate lim(x->0) 1/x ...we write the answer that LHL is -inf and RHL is +inf...we can say undefined because infinity is not defined!
But what is f(0)? .... it is said to be not defined and NOT INFINITY!!!!
Note that lim(x->a) f(x) means that what value does f(x) APPROACH as x APPROACHES a... x is never equal to a and f(x) is never equal to the answer we get...
This 1/0 concept used to be wrong in previous NCERT books too...but it has been corrected...