Difference between the definitions of connected and bipartite graphs

Question

The question which I am about to ask is closely related with this one.

Question: In the definition of bipartite graphs we consider partitions $X, Y$ to be any subset of $V$. If we require them to be nonempty, then in this case as far as I understand the graph $G=(V,E)$ with $|V|=0,1$ and $E=\varnothing$ is NOT bipartite. If I am wrong please correct me.

But why in the definition of connected graphs we do require $X,Y$ be nonempty?

Answer 1

If you did not require $X$ to be nonempty, then every graph would be disconnected: take $X=\emptyset$ and $Y=V$.

If you did not require $Y$ to be nonempty, then every graph would be disconnected: take $X=V$ and $Y=\emptyset$.