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Galileo's Paradox
are there as many squares as numbers?
Some counting numbers are perfect squares: 1, 4, 9, 16 and so on. Most numbers are not squares; from 1 to 100 only 10 of them are. So it seems there are fewer squares than counting numbers. But every counting number can be paired with exactly one square: 1 with 1, 2 with 4, 3 with 9, 4 with 16, forever. Galileo wrote about this in 1638.
Source: A classic puzzle, retold by INFINITE SUM and fact-checked against our curated notes
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