on theotherhandasdesiredwe mayassumeotherwisesupposewhich iswhat wewantedhenceon thecontrarywithoutloss ofgeneralityby thefundamentaltheorem of___runs outofalphabetsto useitsufficesto showwe needto showsuchthatassume for acontradictionQ.E.Dclearlylots ofhandwavingso wearedoneETSobservelet x bearbitrarynoticewe firstprove thefollowinglemmaon theotherhandasdesiredwe mayassumeotherwisesupposewhich iswhat wewantedhenceon thecontrarywithoutloss ofgeneralityby thefundamentaltheorem of___runs outofalphabetsto useitsufficesto showwe needto showsuchthatassume for acontradictionQ.E.Dclearlylots ofhandwavingso wearedoneETSobservelet x bearbitrarynoticewe firstprove thefollowinglemma

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