can someone explain why *exactly* this proof doesn’t work for an infinite number of sets? usually when we prove things with induction they work “all the way” so what’s the concrete thing stopping the train here? 
ok i see. so we can only use induction because we have "n" here. and we show that it works for all n. however, whichever n we pick, it’s finite. so we’ve only shown this works for all finite sets.
for an infinite set, we have to get rid of "n", but then we can’t induct on it...
for an infinite set, we have to get rid of "n", but then we can’t induct on it...
in other words, just because induction lets us generate an infinite number of proofs, none of these proofs are constructing infinite objects by themselves
i’m glad i’ve decided to spend 30 minutes trying to figure this out (with your help). worth it
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