It seems that posits have a value called NaR ("not a real") which serves the purpose of all the special values (including both infinities) in IEEE floats. There

It seems that posits have a value called NaR ("not a real") which serves the purpose of all the special values (including both infinities) in IEEE floats. There are some key differences though: NaR (posits) NaN (floats) ------------ ------------ one bit pattern many different bit patterns always equal to itself never equals itself less than all other values falsifies all orderings