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Surjection
/sɜːˈdʒɛkʃən/noun
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A surjection is a function that maps elements from one set to another such that every element in the target set is hit by at least one element from the source set, making it 'onto' and ensuring complete coverage. In modern mathematics, it's essential for concepts like inverses and equivalences, but it doesn't guarantee one-to-one pairings, which can lead to fascinating paradoxes in infinite sets.
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Surjections reveal the mind-bending nature of infinity; for example, the function that maps all natural numbers to even numbers is a surjection, proving there are exactly as many even numbers as all natural numbers combined, a concept that baffled early mathematicians like Galileo.
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