Is a glass half empty or half full?

You see, there are a few questions like this and now I try to mathematically solve the riddle…but do you agree with my resulting conclusion?

Empty means there is nothing there…we all know that half of nothing is nothing. A full glass is one glass full…half of one full glass is half So, surely half empty is incorrect (as half of nothing is nothing) and the glass is truly half full (half of a full (one) glass or half of a full…or half full).
I have tried to give mathematical reasoning for this which is why it is posted in math. *>rolling eyes smiley posted here<*. Even now many do not understand the spirit of the question. ^^ I know it has been posted before, I ALREADY STATED THAT but it is definately not the same question. Thanks to those who answered with a mathematical mind. 😀