Formal Theory
Formally, a string is a finite sequence of symbols such as letters or digits. The empty string is the extreme case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments, the empty string is denoted with λ or sometimes Λ or ε.
The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string.
The empty string has several properties:
- . The string length is zero.
- . The empty string is the identity element of the concatenation operation (which forms a free monoid on the alphabet Σ).
- . Reversal of the empty string produces the empty string.
- The empty string precedes any other string under lexicographical order, because it is the shortest of all strings.
Read more about this topic: Empty String
Famous quotes containing the words formal and/or theory:
“True variety is in that plenitude of real and unexpected elements, in the branch charged with blue flowers thrusting itself, against all expectations, from the springtime hedge which seems already too full, while the purely formal imitation of variety ... is but void and uniformity, that is, that which is most opposed to variety....”
—Marcel Proust (1871–1922)
“Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.”
—H.L. (Henry Lewis)