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Math and science::Analysis::Tao::06. Limits of sequences

Subsequences and limits, proposition

Subsequences and limits

Let (an)n=0 be a sequence of real numbers, and let L be a real number. Then the the following two statements are logically equivalent:

  • The sequence (an)n=0 converges to L.
  • [...]

Subsequences related to limit points

Let (an)n=0 be a sequence of real numbers, and let L be a real number. Then the following two statements are logically equivalent:

  • [...]
  • There exists a subsequence of (an)n=0 which converges to L.