Can we graph $x^{\infty}-y^{\infty}=1$

Can we graph $x^{\infty}-y^{\infty}=1$

Playing around with exponents on $x^{n}-y^{n}=1$ suggests a trend toward
cleaner and cleaner corners as n increases on one graph for even numbers
and a second graph for odd numbers. Therefore, is it possible to graph the
case of $n=\infty$ for odd and/or even numbers (separately)?