# Is "$--2$" by itself a valid Math expression?

I inserted the following in the calculator:

$$--2$$

and the calculator gave me a result of $$2$$.

Is $$--2$$ by itself a valid Math expression, or did the calculator added $$0$$ or something before it (e.g.. the calculator might have turned $$--2$$ into $$0--2$$)?

• You can think of $"-"$ as an operator you can apply to any number to obtain the additive inverse. So you can apply it to $-2$. This is formalised in group theory, for example, where one of the group axioms is that every element has an inverse [technical note: other axioms exist, but they are equivalent]. Commented Sep 28, 2020 at 17:41

There is nothing wrong with this. It may be interpreted as $$-(-2)$$, which is $$2$$. If the calculator somehow inserted a $$0$$, it is still right since $$0 - (-2)= 0+2=2$$.
If you're okay with negatives, think of $$-(-2)$$ as $$(-1)(-1 \cdot 2)$$ and note that $$(-1)\cdot(-1)=1$$, so you just get $$2$$ at the end.
It is the additive inverse of the additive inverse of two. That is, we have $$(--2)+(-2)=0$$ by definition, so that $$(--2)-2=0\implies --2=2.$$
$$--2$$ is equivalent to $$-(-2)$$ or $$-1 \cdot (-1 \cdot 2)$$.
$$-1 \cdot -1$$ is just $$1$$, so we get $$1 \cdot 2$$, which is equal to $$2$$.