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A databases book I am using states [1]:

The closure of {A1, A2, ..., An} under the FD's in S is the set of attributes B such that every relation that satisfies all the FD's in set S also satisfies A1 A2 ... An -> B.

I'm not trying to nitpick, but shouldn't it say "...the set of all attributes B..." or am I reading it too strictly? The blockquote above seems to indicate any attribute functionally determined by {A1, A2, ..., An} is a closure, yet the algorithms given later in the text seems to define a closure as all attributes functionally determined.

[1] Ullman, Jeffrey D., and Jennifer Widom. A first course in database systems. 3rd ed. Upper Saddle River, NJ: Pearson/Prentice Hall, 2008.

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