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When has one sufficiently mastered an area of mathematics?

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( 4 months ago )

This is a rather soft question regarding the mastery of various mathematical subjects, such as undergraduate subjects.

In particular, say, when has one mastered undergraduate analysis? Is it realistic to expect some individual to be able to prove every theorem and do every exercise in Baby Rudin? What about analysis not covered in Baby Rudin? Say, should one also be able to prove compactness is equivalent to sequential compactness, and sequential compactness is equivalent to closed and boundedness in 

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