we firstprove thefollowinglemmasuchthatassume for acontradictionnoticeclearlysupposeobserveon theotherhandwithoutloss ofgeneralityso wearedonelots ofhandwavingby thefundamentaltheorem of___we mayassumewe needto showhenceruns outofalphabetsto useon thecontrarywhich iswhat wewantedotherwiseitsufficesto showasdesiredETSQ.E.Dlet x bearbitrarywe firstprove thefollowinglemmasuchthatassume for acontradictionnoticeclearlysupposeobserveon theotherhandwithoutloss ofgeneralityso wearedonelots ofhandwavingby thefundamentaltheorem of___we mayassumewe needto showhenceruns outofalphabetsto useon thecontrarywhich iswhat wewantedotherwiseitsufficesto showasdesiredETSQ.E.Dlet x bearbitrary

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