Multiplication is by definition information conserving. We have: \(\delta(a \times b) = 0\), since \(\log (a \times b) = \log a + \log b\). Still multiplication does not preserve all information in its input: the order of the operation is lost. This is exactly what we want from an operator that characterizes an extensive measure: only the extensive qualities of the numbers are preserved. If we multiply two numbers \(3 \times 4\), then the result, 12, allows us to reconstruct the original computa