Formal languages are introduced as subsets of the set of all 0-based finite sequences over a given set (the alphabet). Concatenation, the n -th power and closure are defined and their properties are shown. Finally, it is shown that the closure of the alphabet (understood here as the language of words of length 1) equals to the set of all words over that alphabet, and that the alphabet is the minimal set with this property. Notation and terminology were taken from [5] and [13]. MML identifier: FLANG 1 , version: 7.8.04 4.81.962
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[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
[2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.