Forum game: Paradoxes!

So I checked out some of the threads in off-topic, and I found toxic132's post about riddles. And I thought: "what about making the same thing.. With paradoxes?" So, what you gotta do is post any kind of paradox you know. I don't mean long ones, I mean short sentences like:
"If a person told you he was lying, would you believe him?"
Or,
"If a set contains all sets, would it contain itself?"

You can then admire someone's paradox, think about it, or, even post an answer!
if you don't know what a paradox is, it's either a long paragraph or a simple "saying" that will make your mind blow.. Literally! It will keep you thinking for hours until you think of an answer!
so, to recap, if you simply heard any (try not to google please!) just post it below.
Have fun!
 
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A guy goes back in time to kill grandpa. Due to that, he is never conceived. Because he is never conceived, he never kills his grandpa.
 
A guy goes back in time to kill grandpa. Due to that, he is never conceived. Because he is never conceived, he never kills his grandpa.
so if he never killed grandpa then he does exist but if he exists then he will kill grandpa but then he wont but.........MINDBLOWN
 
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.
[JFrater: I will point out the problem with this paradox to give you all an idea of how the others might be wrong: in physical reality it is impossible to transverse the infinite - how can you get from one point in infinity to another without crossing an infinity of points? You can't - thus it is impossible. But in mathematics it is not. This paradox shows us how mathematics may appear to prove something - but in reality, it fails. So the problem with this paradox is that it is applying mathematical rules to a non-mathematical situation. This makes it invalid.]
 
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