The problem arises with the way that this stuff is taught at a very elementary level, which then needs to be thrown away and relearned long after intuition and

The problem arises with the way that this stuff is taught at a very elementary level, which then needs to be thrown away and relearned long after intuition and habits have formed around the old model. As an adult my reasoning is that it does indeed only do one thing: negation. it doesn't take anything away at all, if anything it actually adds information. Negating a four doesn't take it away, it just specifies a different (inverted) mapping of a given value with respect to zero. And this is still a very naive take, as someone with no background in number theory. But it's much more useful than say, Billy has four apples, he gives three to Mary, etc.