The math jargon for a set where you can implement a 4 function calculator $$(+,-,*,/)$$ is a field. Fields can have a finite number of elements, and such fields always have a prime power number of elements, aka $$p^k$$ where $$p$$ is prime and $$k$$ is a natural number.

Many results are not true if the underlying field has exactly 2 elements. The reason why:

$$x = -x$$ $$x + x = -x + x$$ $$2x = 0$$

The final formula is taken to mean that $$x$$ is zero. But there’s another interpretation.

What if 2 = 0?

In a field with 2 elements, this is true. Moreover, $$x = -x$$ is a tautology AKA always true AKA worthless. $$-1 \mod 2 = 1$$ and $$0 \mod 2 = 0$$.

This is only when the underlying field has 2 elements. A 2 element set is exceptional because negation doesn’t actually do anything.