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:
“The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.”
—Edgar Lee Masters (1869–1950)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)