we mayassumesuchthatasdesiredobservewe firstprove thefollowinglemmalet x bearbitrarywithoutloss ofgeneralitysupposeruns outofalphabetsto useassume for acontradictionon theotherhandwhich iswhat wewantedby thefundamentaltheorem of___noticeitsufficesto showclearlyotherwiseQ.E.Dhenceon thecontrarylots ofhandwavingETSwe needto showso wearedonewe mayassumesuchthatasdesiredobservewe firstprove thefollowinglemmalet x bearbitrarywithoutloss ofgeneralitysupposeruns outofalphabetsto useassume for acontradictionon theotherhandwhich iswhat wewantedby thefundamentaltheorem of___noticeitsufficesto showclearlyotherwiseQ.E.Dhenceon thecontrarylots ofhandwavingETSwe needto showso wearedone

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