Prove this number fact Prove that $x \neq 0,y \neq 0 \Rightarrow xy \neq 0$. 
Suppose $xy = 0$. Then $\frac{xy}{xy} = 1$. Can we say that $\frac{xy}{xy} = 0$ and hence $1 = 0$ which is a contradiction? I thought $\frac{0}{0}$ was undefined. 

consider that xy=0 from the  basic  axioms we know that  product is zero  when  at least one of the  multiplier is  zero  so is means that  x is zero or y is zero  or both x and y is equal zero  which contradicts  to given condition that neither x or y is zero so it means that their product is also  not equal to zero
