Interesting Paradox

Can you prove that any gun in world can never fire a bullet ?

Yes, a simple paradox given by Aristotle indeed proves that by taking help of logic ! It's known as dichotomy paradox. The conjecture is as follows -

Suppose you fire a bullet from place 'A' and that bullet hits the target at place 'B'. It's obvious that, before reaching to point 'B' that bullet has to travel to halfway point between A and B. Let's say this point is 'C'. Applying the same logic, to reach to piont 'C' the bullet has to first travel to halfway point, say 'D', between points A and C. You can go on applying this logic unendingly because space is infinitely divisible, and you will always find a point halfway between any given two points !

So logically, indeed your halway point will reach very close to starting point of the bullet but never reach to starting point exactly. And hence your bullet will never start off from the gun -:)