Definition:String

Let $$\mathcal{A}$$ be an alphabet of symbols.

A string (in $$\mathcal{A}$$) is a sequence of symbols from $$\mathcal{A}$$.

There is no limit to the number of times a particular symbol may appear in a given string.

Finite String
A finite string is a string with a finite number of symbols in it.

Null String
A null string is a string with no symbols in it at all.

Length
The length of a string is the number of symbols it contains.

Thus a null string has a length of $$0$$.

The length of a string $$S$$ can be denoted $$\operatorname {len} \left({S}\right)$$ or $$\left|{S}\right|$$.

Initial Part
A string $$T$$ is an initial part of a string $$S$$ if $$T$$ is formed by removing one or more symbols from the end of $$S$$.

Proper Initial Part
A string $$T$$ is a proper initial part of a string $$S$$ if $$T$$ is an initial part of $$S$$ and is not a null string.

Concatenation
We use the notation $$S T$$ to mean the string $$S$$ followed by the string $$T$$.

That is, $$S T$$ is $$T$$ concatenated with $$S$$.

Length of Concatenation
Clearly $$\left|{S T}\right| = \left|{S}\right| + \left|{T}\right|$$.