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To take a limit you need a topology. There is no standard topology on 'the set of all sets'. So I suggest explaining to the reader what your definition of 'limit of a set' is.dimitri151 said:p.s. You can take the limit of a set. Happens all the time.
The G-delta Set Theorem is a mathematical theorem in set theory that states that every set that can be written as a countable intersection of open sets is a G-delta set, meaning it is the intersection of a countable collection of open sets.
The G-delta Set Theorem is important because it allows for the study and classification of certain types of sets in mathematics. It also has applications in other areas such as topology and measure theory.
The proof of the G-delta Set Theorem involves using the definition of a G-delta set and showing that it is equivalent to the countable intersection of open sets. This can be done using the properties of open sets and basic set theory.
Some examples of G-delta sets include the set of rational numbers, the set of real numbers, and the set of all continuous functions on a given interval. Basically, any set that can be written as a countable intersection of open sets is a G-delta set.
The G-delta Set Theorem has implications in other areas of mathematics, such as measure theory, topology, and functional analysis. It allows for the study and classification of different types of sets, which can be useful in solving various mathematical problems.