Collection of Finite Subsets is Countable

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We prove that the set consisting of finite subsets of a countable set is countable. This is a useful fact in math competitions such as the Putnam math competition.

  1. Dr. Ebrahimian
  2. Math
  3. maths
  4. Set Theory
  5. Countable
  6. Uncountable
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Комментарии
Автор

Much better than the other proofs of this I've seen. Way more intuitive and uses easily provable results

yajaman
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You just saved me from getting an F on my real analysis final Dr. Ebrahimi! Much appreciated!

parsashirani
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I like it. Here is a sketch of another way. Our base countable set is isomorphic to the Natural numbers. Define a map that takes any finite subset of natural numbers to the the product of all the primes indexed by elements of the subset, e.g. {1, 3} maps to 2*5=10. {1} maps to the empty set.

petersiracusa
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hey i have a doubt! in 4:24, while writing the expression for Sn+1 in terms of union, we have A belongs to Sn right? but Sn also has many other elements, so what about their union with {Xk} ?

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