"Forget infinity; divide the number 1 by 2 forever and you still wont reach zero, EVER! Do you need an education to realise that?"
Slight miscommunication.
It doesn't have to reach. It "tends to" zero, in the jargon. That's why in math, we use the limit:
lim (x-c)/[(x-a)(x-b)]
n->inf
What is it "in the limit," regardless of whether that limit is ever reached. As n "increases without bound," the value of the function approaches zero. (This should be intuitive, but you can also use L'Hopital.)
OTOH, there is a semantic gap in that mathematics doesn't necessarily have to correspond to our physical reality - and vice versa.
I disagree with your assertion that nothing exists unless it has weight. I think that's far too specific a definition. A slightly better one might be that nothing exists unless it is capable of producing "some (putatively) observable effect on something else."
Yours is a dangerous assertion in that there's no justification for it. We might as well declare that nothing can be said to exist unless it's made of peanut butter.
The argument about not having an instrument fine enough to measure (either weight or mass) of a photon is also flawed (not just on lack of evidence, but of even being scientifically legitimate) unless you can propose an experiment that might prove you're wrong, if you are wrong.
