suchthatwhich iswhat wewantedotherwiseETSso wearedonesupposewithoutloss ofgeneralitynoticeitsufficesto showwe mayassumeobservelots ofhandwavingwe needto showasdesiredclearlyby thefundamentaltheorem of___on thecontraryon theotherhandlet x bearbitraryhenceruns outofalphabetsto useassume for acontradictionQ.E.Dwe firstprove thefollowinglemmasuchthatwhich iswhat wewantedotherwiseETSso wearedonesupposewithoutloss ofgeneralitynoticeitsufficesto showwe mayassumeobservelots ofhandwavingwe needto showasdesiredclearlyby thefundamentaltheorem of___on thecontraryon theotherhandlet x bearbitraryhenceruns outofalphabetsto useassume for acontradictionQ.E.Dwe 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. such that
  2. which is what we wanted
  3. otherwise
  4. ETS
  5. so we are done
  6. suppose
  7. without loss of generality
  8. notice
  9. it suffices to show
  10. we may assume
  11. observe
  12. lots of handwaving
  13. we need to show
  14. as desired
  15. clearly
  16. by the fundamental theorem of ___
  17. on the contrary
  18. on the other hand
  19. let x be arbitrary
  20. hence
  21. runs out of alphabets to use
  22. assume for a contradiction
  23. Q.E.D
  24. we first prove the following lemma