hence it suffices to show let x be arbitrary on the contrary we may assume as desired suppose without loss of generality assume for a contradiction such that which is what we wanted so we are done otherwise clearly we first prove the following lemma ETS by the fundamental theorem of ___ on the other hand observe Q.E.D runs out of alphabets to use notice we need to show lots of handwaving hence it suffices to show let x be arbitrary on the contrary we may assume as desired suppose without loss of generality assume for a contradiction such that which is what we wanted so we are done otherwise clearly we first prove the following lemma ETS by the fundamental theorem of ___ on the other hand observe Q.E.D runs out of alphabets to use notice we need to show lots of handwaving
(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.
hence
it suffices to show
let x be arbitrary
on the contrary
we may assume
as desired
suppose
without loss of generality
assume for a contradiction
such that
which is what we wanted
so we are done
otherwise
clearly
we first prove the following lemma
ETS
by the fundamental theorem of ___
on the other hand
observe
Q.E.D
runs out of alphabets to use
notice
we need to show
lots of handwaving