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Some of the oldest methods of telecommunications implicitly use many of the ideas that would later be quantified in information theory. Modern telegraphy, starting in the 1830s, used Morse code, in which more common letters (like "E", which is expressed as one "dot") are transmitted more quickly than less common letters (like "J", which is expressed by one "dot" followed by three "dashes").
It is common in information theory to speak of the "rate" or "entropy" of a language. This is appropriate, for example, when the source of information is English prose. The rate of a source of information is related to its redundancy and how well it can be compressed, the subject of source coding.
In information theory, one bit is the information entropy of a random binary variable that is 0 or 1 with equal probability, [3] or the information that is gained when the value of such a variable becomes known. [4] [5] As a unit of information, the bit is also known as a shannon, [6] named after Claude E. Shannon.
Charles S. Peirce's theory of information was embedded in his wider theory of symbolic communication he called the semiotic, now a major part of semiotics. For Peirce, information integrates the aspects of signs and expressions separately covered by the concepts of denotation and extension , on the one hand, and by connotation and comprehension ...
The violet is the mutual information (;) . Venn diagram of information theoretic measures for three variables x, y , and z . Each circle represents an individual entropy : H ( x ) {\displaystyle H(x)} is the lower left circle, H ( y ) {\displaystyle H(y)} the lower right, and H ( z ) {\displaystyle H(z)} is the ...
There is an analogy between Shannon's basic "measures" of the information content of random variables and a measure over sets. Namely the joint entropy , conditional entropy , and mutual information can be considered as the measure of a set union , set difference , and set intersection , respectively (Reza pp. 106–108).
Information can be defined exactly by set theory: "Information is a selection from the domain of information". The "domain of information" is a set that the sender and receiver of information must know before exchanging information. Digital information, for e
The (standard) Boolean model of information retrieval (BIR) [1] is a classical information retrieval (IR) model and, at the same time, the first and most-adopted one. [2] The BIR is based on Boolean logic and classical set theory in that both the documents to be searched and the user's query are conceived as sets of terms (a bag-of-words model).