I've just been going through an equation, which is as follows:
$(x+4)^2 = 16$
Lets work through it:
$$x^2 + 8x +16 = 16$$ $$x^2 +8x = 0$$ $$x^2 = -8x$$ $$x = -8$$
However, as i've just found out, $0$ is also a solution, as $0 = -8$. Oh wait, no it doesn't.. And yet, $0^2 + 8 \times 0 + 16 = 16$.
What's going on here though? Does $0$ even matter? It's true that $16 = 16$, but it's not true that $0 =-8$. But maybe $16$ equals $16$, not because $-8^2 - 8 \times 8 = 0$, but just because $16$ equals to itself, independent of $0$.
I think it's interesting to draw a parallel between the falsity of the final solution (when $x = 0$), and the fact that nothing, represented by $0$, literally doesn't seem to exist in the real world.
Is $0$ ever used however? In either pure mathematics for a particular proof, or perhaps within the domain of science? I suppose one use of $0$ would be to do a 'hard reset', for whatever reason, but then again, you could just do that without $0$, I suppose.
Furthermore, maths in supposed to be consistent, and since the consistency of mathematics seems to be disrupted by the usage of $0$, does that mean $0$ is somehow 'dangerous'. My example here was simple, but what if you were say, launching a rocket to space, where lives are on the line. Can you trust $0$?