In our dots-and-boxes machines we’ve been working with dots, which we draw as solid dots.
We now need the notion of the opposite of dot.
Like matter and antimatter, which annihilate when brought together, a dot and an antidot should also annihilate – POOF! – when brought together to leave nothing behind.
Let’s draw antidots as hollow circles.
If a dot represents , then an antidot represents , and bringing one of each together leaves zero.