suchthatwe firstprove thefollowinglemmawhich iswhat wewantedwe mayassumesupposeby thefundamentaltheorem of___itsufficesto showclearlyhencelet x bearbitraryassume for acontradictionon thecontraryruns outofalphabetsto useso wearedoneobservenoticeotherwiseETSasdesiredwithoutloss ofgeneralitylots ofhandwavingon theotherhandwe needto showQ.E.Dsuchthatwe firstprove thefollowinglemmawhich iswhat wewantedwe mayassumesupposeby thefundamentaltheorem of___itsufficesto showclearlyhencelet x bearbitraryassume for acontradictionon thecontraryruns outofalphabetsto useso wearedoneobservenoticeotherwiseETSasdesiredwithoutloss ofgeneralitylots ofhandwavingon theotherhandwe needto showQ.E.D

Your last - Call List

(Print) Use this randomly generated list as your call list when playing the game. There is no need to say the BINGO column name. Place some kind of mark (like an X, a checkmark, a dot, tally mark, etc) on each cell as you announce it, to keep track. You can also cut out each item, place them in a bag and pull words from the bag.


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  1. such that
  2. we first prove the following lemma
  3. which is what we wanted
  4. we may assume
  5. suppose
  6. by the fundamental theorem of ___
  7. it suffices to show
  8. clearly
  9. hence
  10. let x be arbitrary
  11. assume for a contradiction
  12. on the contrary
  13. runs out of alphabets to use
  14. so we are done
  15. observe
  16. notice
  17. otherwise
  18. ETS
  19. as desired
  20. without loss of generality
  21. lots of handwaving
  22. on the other hand
  23. we need to show
  24. Q.E.D