The set of positive integers under addition has closure because it goes on for infinity and you will always have the element $a + b$. I am also aware that addition is associative but do we include $0$ in this group? It is neither positive nor negative so I would have assumed not.
I've been given the answer by a textbook that there is "No inverse of $-1$". But I don't even see how that relates the set of positive integers. My answer would have been that there was no identity or that all the elements do not have an inverse.
Could someone clarify this please?