 Multiplying or dividing an infinite number by a finite positive number leaves it unchanged, and multiplying or dividing by a finite negative number reverses its sign. Similarly for multiplying the infinite numbers by themselves or each other. But an infinite number divided by an infinite number, or an infinite number multiplied by 0, are also indeterminate forms. As \(x\) approaches 0, the function \(\frac{1/x^2}{1/x^2}\) has limit 1, while the function \(\frac{1/x^2}{1/x^4}\) has limit \(+\infty\). If we take the function \(1/x^2\) whose limit is \(+\infty\) and multiply it by the function \(x\) whose limit is 0, we get the function \(1/x\), that has no limit as \(x\) approaches 0 (since it takes on both large positive and large negative values in any small interval around 0—this is why we have used \(1/x^2\) and \(1/x^4\) as the paradigms of functions with limit \(+\infty\), rather than \(1/x\) or \(1/x^3\)). For similar reasons, these extended real numbers don’t provide a way to divide by 0. So although the extended real numbers have some nice properties, and can be used for measurement in various cases, arithmetic involving them is not as nice as the standard real numbers.