Definition:Empty Set/Historical Note
Historical Note on Empty Set
The use of $\O$ has relevance to the computing industry, when $\emptyset$ is usually used in the rendering of source code to mean "zero", in order to distinguish it from $\mathrm O$ (the letter O).
In the same context, the letter O was sometimes seen rendered as $\odot$, so as to ensure its being differentiated from "zero".
The latter has fallen out of use, but it is still common for mathematicians, when writing their mathematics by hand, to strike through their zeroes out of habit.