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Uhmm, that is not my confusion, but rather "any maximal intersecting family can be changed into any other". For example given the base set [1,...,n], and we take all of the sets that contain 1, how can we turn this into the family where all of it's sets contain 2? How to do it in general, is there an "algorithm" for it?
the last sentence in the paragraph is interesting, can you point me to a lecture/something that explains how to do it? I know this post was 7 years ago, so maybe someone else can also point me towards the right direction..
