E.g. my friend was confused when he read an exercise telling him to prove that a set was “the smallest set” with this property (and perhaps obviously the author didn’t unpack this). What this means formally when expanded is “Prove that this set is a subset of every set with this property.” AFAICT, there’s no way to figure out what this means formally without someone telling you, or (this is unlikely) inventing the formal version yourself because you need it and realizing that ‘smallest set’ is good shorthand and this is probably what was meant.
Slight nitpick: it means “prove that this set is a subset of every set with this property, and has this property.”
This sort of thing is terrible; I learned most of it from the internet (MathOverflow, Wikipedia, the nLab, blogs), for what it’s worth.
Slight nitpick: it means “prove that this set is a subset of every set with this property, and has this property.”
This sort of thing is terrible; I learned most of it from the internet (MathOverflow, Wikipedia, the nLab, blogs), for what it’s worth.