Definition:Substring

Definition
Let $$\mathcal L$$ be a formal language with alphabet $$\mathcal A$$.

Let $$S$$ be a string in $$\mathcal A$$.

Let $$T$$ be a string in $$\mathcal A$$ such that:
 * $$S = S_1 T S_2$$

where:
 * $$S_1$$ and $$S_2$$ are strings in $$\mathcal A$$ (possibly null);
 * $$S_1 T S_2$$ is the concatenation of $$S_1$$, $$T$$ and $$S_2$$.

Then $$T$$ is called a substring of $$S$$.

It follows from this definition that $$S$$ is a substring of itself (by considering $$S_1$$ and $$S_2$$ as both null).

Also see

 * The initial part of a string $$S$$ is a substring of $$S$$.