Although that is no absolute set of symbols in mathematics some notations are widely accepted. The symbol is used to denote the real numbers. denotes the positive reals and denotes the negative reals.
Thus so the nonnegative reals are .
As to the “Was I totally wrong?”, I really have no idea what you did. I cannot follow it. The symbolic statement reads “There is some nonnegative real number, x, having the property that for every real number y then .
You see that zero has that property; so does .