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0rthodontist

Science Advisor

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Is there a general good way to represent sets as sequences, without wasting data or conveying extra data? One way is a membership list like 11010100111010 but this only works if the possible number of elements is small. I am thinking, data _other_ than ordering, directly about the set objects, can be conveyed through ordering. Like if I'm talking about a set of eleven ten-digit numbers, and one of them has all distinct digits, then I can list the other 10 numbers in an order according to the digits of the 11th number, and from that list of 10 numbers all 11 can be reconstructed and the list does not seem to convey any extra information. Is there a general way to do this for any set of numbers?

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