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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.”
—Thomas Carlyle (1795–1881)