[QUOTE=Really Not All That Bright]
Looked for old threads on this, but none that I found were asking the exact question.
A long time ago, my French teacher (don’t ask why) pointed out the following paradox to my class.
If we believe space is infinitely divisible, then… QUOTE]
The answer (no, I’m not looking below to see all the other correct responses! 
) is that space isn’t infinitely divisible.
Sorry for the messed up coding. And an incomplete response, to boot!
Anyway, in addition to the sum of infinities (which is also another correct way to look at it), the fact that space isn’t infinitely divisible means that there comes a time in which the bullet can’t travel “half the distance”, and therefore hits you. IIRC, the smallest distance possible is 10^-33 centimeters.
It’s not a bullet. It’s a 420’s BCE-style paradoxical death ray.
Or you could aim your gun at a point that’s twice as far away as your target’s head, so that by the time you start halving the distance, your teacher’s already history, or something
maybe
The interesting thing about this thread is that not only was the OP answered simultaneously by a slew of posters in a matter of minutes, but another slew of posters came along equally quickly to comment on the quickness of the simulposts.
Now here’s the real paradox - if there is an infinite amount of potential posts between a Doper clicking “Submit Reply” and Dopers 'round the world actually reading the first Doper’s post in time to acknowledge it, and that infinite potential can be condensed into a finite number of actual posts, what happens to the rest of infinity?
There’s a nice geometric way of (partially) convincing yourself that an infinite series can be summed to a finite number. Take a piece of paper and draw a square. Half the square. Now half one of the halves. Half one of those halves etc. Imagine that you do this infinitely often - you have an infinity of subsquares contributing to make a single, finite square.
(Not stating anything new, just phrased different.)
By dividing the movement of the bullet into halves, all you’re doing is determining it’s position at various times. If I have a formula like y=x then I can calculate y for any given x. There’s an infinite number of x’s that I can plug in there; I can go all the way from negative infinity to infinity, or I can go through all the fractions between 0 and 1. But just because there are an infinite number of potential x’s between 0 and 1, doesn’t mean that x never reaches 1. x isn’t a moving object, it’s just a number in a formula. Similarly, while your bullet is an object, it’s position in relation to time is just a formula. So yes, you can calculate all you want down to the smallest fractions of a second, but just because you are spending a lot of time calculating positions doesn’t mean that the formula doesn’t carry on through to the position at which the bullet touches nipple.
And of course, 0.9999… = 1.
I think it’s called Rio, by Duran Duran.
It’s a mathematical thought experiment, not a question of physics or physical space. A sum of infinities is the only way to look at it.
Not until Karl Gauss and QtM post.
BUT WAIT! Time can be infinitely halved as well.
11:59.00 p.m.
11:59.50 p.m.
11:59.75 p.m.
11:59.875 p.m.
So, I wouldn’t worry about your nipple.
We can give Zeno a pass because he lived 2500 years ago. But calculus has been around for three hundred years; even a French teacher should have gotten the word by now that an infinite series can add up to a finite total.
I have a question: Is it some sort of paradox, and does that paradox have a name of any kind?
Read post #5.
Not only will the bullet reach its target in a finite time, but it will make a whooshing noise. 
I think Zeno’s paradoxes can actually be adequately summarised by the phrase “Look, just hurry up and invent calculus, willya?” - It’s clear that’s what he was grasping for.
As a teacher, I find this quite depressing.
Couldn’t the french teacher be bothered to ask a physics (or maths) colleague?
Given that things thrown fast + accurately enough do hit their target, why not try to work out what is going on?
I remember the delight of realising that this way of looking at things showed that the infinite series 1+0.5+0.25… must sum to 2.
So as it turns out, I’m the only poster on the board who doesn’t know what Zeno’s paradoxes are, and I’m certainly the only one who didn’t post said information to this thread in a four-minute period.
That was quite impressive, and thank you all. I understand the sum of infinities part, but is…
…quite right?
I don’t think he was asking us for the answer, just trying to get us to think.