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While using L' Hospital's rule in evaluating limits, one comes across limits of the following type: $$\lim_{x \to 0} x \ln x$$ Such limits are generally evaluated by taking ##x## to the denominator and make it ##x^{-1}##. In such a case, an indeterminate form ##\frac{\infty}{\infty}## comes, which can be evaluated by L' Hospital's rule.

But logarithmic function is not defined for ##x=0##, because no power can make a number 0.

Books are doing these types of sums by taking ##\ln 0 = \infty##.

But is it correct to say that anything that is undefined, is infinity? Infinity is undefined, but that does not mean that anything that is undefined, is infinity. Infinity is a concept, not a number that we can play with.

N.B.: My problem is not a homework problem. I am asking whether the above concept is actually correct, and it has no direct connection with a particular sum in any book.

But logarithmic function is not defined for ##x=0##, because no power can make a number 0.

Books are doing these types of sums by taking ##\ln 0 = \infty##.

But is it correct to say that anything that is undefined, is infinity? Infinity is undefined, but that does not mean that anything that is undefined, is infinity. Infinity is a concept, not a number that we can play with.

N.B.: My problem is not a homework problem. I am asking whether the above concept is actually correct, and it has no direct connection with a particular sum in any book.

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