Null String has Length Zero

Definition

Let $\epsilon$ denote the null string.

Then:

$\size \epsilon = 0$

where $\size \epsilon$ denotes the length of $\epsilon$.

Proof

Follows directly from the definitions of null string and string length.

$\blacksquare$

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
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.3$: Induction on Length of Wffs