Empty Set forms Formal Language
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Example of Formal Language
The empty set $\O$ forms a formal language.
Proof
$\O$ vacuously forms a set of symbols.
Similarly, the formal grammar is vacuous.
The result follows by definition of formal language.
$\blacksquare$
Also see
- Set of Null Strings forms Formal Language: a different formal language from this one
Sources
- 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.1$ Strings, Alphabets and Languages