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by ufo
1154 days ago
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For finite sets, bijection is equivalent to counting the number of elements. A set of size N has an 1-to-1 mapping to the set {1,...,N}. For infinite sets, counting no longer makes sense but bijection does. From this point of view, the bijection trick is a way to extend the usual notion of set size, so that it also works for infinite sets. That said, it's certainly not an "obvious" idea and in fact it took many years until it was widely adopted by the mathematical community. |
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