 Addition  Addition is associated with information storage in terms of sequences or strings of symbols. It is information discarding for natural numbers bigger than 1. We have \(\delta(a + b) \lt 0\) since \(\log (a + b) \lt \log a + \log b\). Still, addition has information preserving qualities. If we add numbers with different log units we can reconstruct the frequency of the units from the resulting number:   \[\begin{align} 232 &amp; = 200 + 30 + 2 \\ &amp; =  (2 \times 10^2) + (3 \times 10^1) + (2 \times 10^0)\\ &amp; = 100 + 100 + 10 + 10 + 10 + 1 + 1 \end{align} \]  