Definition:String

Definition
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.

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 $$S$$.

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 the length of $$S T$$ is given by:
 * $$\left|{S T}\right| = \left|{S}\right| + \left|{T}\right|$$

Also see

 * Substring
 * Null string
 * Word

Variants
Some sources use the word string to mean a finite string, i.e. what we have chosen to call a word.