Given

$$\frac{1}{\infty}=0$$ (1)

prove

$$\frac{1}{0}=\infty$$ (2)

Proof:

1. Rotate counterclockwise both sides of Eq. (1) by $90^\circ$ to get $-18=0$.
2. Add $8$ on both sides to get $-10=8$.
3. Rotate clockwise both sides by $90^\circ$ to get Eq. (2)

Q.E.D.