Group

A pair $(G,+:G\times G\to G)$ is a group iff

$$\exists 0\in G.\forall x\in G.0+x=x+0=0\text{\hspace{1em}(ident)}$$ $$\forall x,y,z\in G.x+(y+z)=(x+y)+z\text{\hspace{1em}(assoc)}$$