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wheelersbit
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In (Shannon) information theory, information is said to be the log of the inverse of the probability - what is the information content of 1+1=2? Or for that matter any fundamental axiom.
wheelersbit said:To give another example can we say structure in mathematics is what gives this a probability of 1?
Information theory is a branch of mathematics that deals with the quantification, storage, and communication of information. It is closely related to mathematics as it uses mathematical principles to study the properties and limitations of information and communication systems.
Some key concepts in information theory include entropy, channel capacity, and data compression. Entropy measures the uncertainty or randomness of a system, while channel capacity determines the maximum amount of information that can be reliably transmitted through a channel. Data compression involves reducing the size of data without losing important information.
Information theory has many practical applications, such as in data compression algorithms used in computer science, error-correcting codes used in telecommunication systems, and cryptography used in securing sensitive information. It is also used in fields such as neuroscience, biology, and economics to study the flow of information in complex systems.
Some famous theorems in information theory include the Shannon-Hartley theorem, which gives the maximum channel capacity for a given amount of noise, and Shannon's source coding theorem, which states that data can be compressed to almost its entropy without any loss of information. Other notable theorems include the data processing inequality, channel coding theorem, and rate-distortion theory.
Information theory was first introduced by Claude Shannon in the late 1940s and has since evolved into a multidisciplinary field with applications in various industries. In recent years, advancements in technology and the rise of big data have led to new developments in information theory, such as the study of information in complex networks and the application of information theory to machine learning and artificial intelligence.