Question regarding notation involving vector spaces. Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on $u+v=(u_1+v_1+1,u_2+v_2+1),$ $ku=(ku_1,ku_2)$.
Show that $(0,0)\neq0$.
I'm confused by their notation. Can anyone explain?

By $\mathbf{0}$ they mean the zero vector. The zero vector has to be the additive identity in order for $V$ to be a vector space, in other words, $\mathbf{0}$ has to be a vector such that $\mathbf{v}+\mathbf{0}=\mathbf{v}$.
