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Zeno formulated several paradoxes.
Not quite it, but the most understandable one can be stated as follows::
We need to go from one wall to the other across the room. If we walk half the distance, we'll have half left. Then half of the remaining amount – only one-fourth remains. Then half of the rest – that leaves one-eighth. And so on, and so on – there will always be something left, which means that it is impossible to go from one wall to another.
Paradox – because the seemingly logical explanation is easily refuted, everyone can walk through their apartment from one wall to the other.
Other examples (the most famous of which is with Achilles and the tortoise) are based on a similar principle – the illogicality that occurs when infinite and continuous quantities are divided into parts.
But it was only with the advent of higher mathematics and the science of limits, infinity, and so on that they were able to explain or refute these conclusions logically and mathematically.