User:Bender2k14/Unusual Behavior at Infinity

• Sum
  • Riemann series theorem: If an infinite series is conditionally convergent, then its terms can be arranged in a permutation so that the series converges to any given value, or even diverges.
• Sets
  • Hilbert's paradox of the Grand Hotel, where "Every Room Occupied" and "No Vacancy" do not mean the same thing.