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  Note That The Marriage Condition Is That, For Any Subset <math>I</math> Of The Women, The Number Of Men Whom At Least One Of The Women Would Be Happy To Marry (<math>\bigcup {i \in I} T I</math>) Be At Least As Big As The Number Of Women, <math>I \{T_i: i \in I\}</math> It is obvious that this condition is ''necessary'', as if it does not hold, there are not enough men to share between the <math>I</math> women What is interesting is that it is also a ''sufficient'' condition