real analysis - Can someone help me solve this problem please.

For the real numbers $x=0.9999999\dots$ and $y=1.0000000\dots$ it is the case that $x^2

Answer

Since $x=y$ (that is, $y = 0.\overline{9}=\sum_{n=1}^\infty \frac9{10^n}=1=x$), it must be the case that $x^2=y^2$. Thus, your statement is false.