asdesiredclearlyETSlots ofhandwavingon theotherhandruns outofalphabetsto useitsufficesto showsuchthatwe mayassumehencewe needto showlet x bearbitrarywhich iswhat wewantedwithoutloss ofgeneralityassume for acontradictionsupposeotherwiseon thecontraryby thefundamentaltheorem of___observeQ.E.Dnoticeso wearedonewe firstprove thefollowinglemmaasdesiredclearlyETSlots ofhandwavingon theotherhandruns outofalphabetsto useitsufficesto showsuchthatwe mayassumehencewe needto showlet x bearbitrarywhich iswhat wewantedwithoutloss ofgeneralityassume for acontradictionsupposeotherwiseon thecontraryby thefundamentaltheorem of___observeQ.E.Dnoticeso wearedonewe 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. as desired
  2. clearly
  3. ETS
  4. lots of handwaving
  5. on the other hand
  6. runs out of alphabets to use
  7. it suffices to show
  8. such that
  9. we may assume
  10. hence
  11. we need to show
  12. let x be arbitrary
  13. which is what we wanted
  14. without loss of generality
  15. assume for a contradiction
  16. suppose
  17. otherwise
  18. on the contrary
  19. by the fundamental theorem of ___
  20. observe
  21. Q.E.D
  22. notice
  23. so we are done
  24. we first prove the following lemma