Nonaffineness of a punctured affine plane
= Nonaffineness of a punctured affine plane
The <punctured affine plane> $U=\mathbb A_k^2\setminus\{(0,0)\}$ is not an <affine scheme>. On its cover $D(x)\cup D(y)$, <global sections> are $k[x,y]_x\cap k[x,y]_y=k[x,y]$ inside the <field of fractions>. Coprimality of $x$ and $y$ proves this equality. If $U$ were affine, its inclusion into $\mathbb A_k^2$ would be an isomorphism by <affine scheme reconstruction from global sections>, contradicting the omitted point.