It seems like a lot of the difficulties in set theory come from trying to make sense of ordered lists just starting with unordered sets.
Wouldn't it be easier to have ordered lists as the fundamental objects? Or even just an ordered pair?
Then the number 5 could be written as $(0,(0,(0,(0,(0)))))$ for example.
Are there any alternatives to set theory that start with ordered lists or pairs and which derive sets from them instead of the other way round?