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Zeno's Paradoxes
The impossibility of motion.
To get to any destination, you must first get halfway there. To get halfway there, you must get a quarter of the way there, and so on. Since there are an infinite number of these 'halfway' points to cross, how can you ever reach the destination? How can motion even begin?
What philosophers say
Zeno's paradoxes challenge the nature of space, time, and infinity. While mathematically we can solve this with the concept of a convergent series (the infinite sum has a finite value), the philosophical problem remains. It highlights a conflict between our logical model of the world and our sensory experience of it. The development of calculus was partly a response to these very problems.