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## Question

Man one (M1) points a gun at Man two (M2),

M1 states he will shoot.

M2 insists the bullet will never leave the gun.

His logic.

Mathematically speaking, in order for the bullet to reach its target, it must travel 1/2 the distance first.

Likewise, prior to that it must travel 1/2 of 1/2 or 1/4 the total distance.

Then 1/8, 1/16, 1,32, 1/64, 1/128 1/256 and so on..

As the ratio will never reach zero, the bullet can never leave the gun.

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The distance traveled between two of these marks decreases by (1/2)^n

However, assuming the bullet travels at constant velocity (or approximately constant)

the time it takes for the bullet to reach the next mark also decreases by (1/2)^n

The total time it takes to the reach the man is an infinite sum of infinitesimal quantities.

This series converges to a finite value, which is the amount of time taken to reach M2.

There will be an infinite number of these halfway marks between M1 and M2, and yes, the bullet will cross an infinite number of them in finite time.

It is really no surprise that an object is capable of traversing an infinite number of points in finite time since there are an infinite number of points between any two points.

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This in an ancient paradox. The answer is actually simple: the sum of all infinite numbers 1/2^n, where n varies from 1 to infinite is a convergent sum, and it converges to 1. more info:

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