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Drawing on insights from Shannon's (1948) seminal paper on Information Theory, we propose that all measures of segregation and inequality are united within a single conceptual framework. We argue that segregation is fundamentally analogous to the loss of information from an aggregation process. Integration is information loss and segregation is information retention. Specifying the exact theoretical and mathematical relationship between inequality and segregation measures is useful for several reasons. It highlights the common mathematical structure shared by many different segregation measures, and it suggests certain useful variants of these measures that have not been recognized previously. We develop several new measures, including a Gini Segregation Index (GS) for continuous variables and Income Dissimilarity (ID), a version of the Index of Dissimilarity suitable for measuring economic segregation. We also show that segregation measures can easily be adapted to handle persons of mixed race, and describe the Non-Exclusive Index of Dissimilarity (NED) and the Non-Exclusive Entropy Index of Segregation (NEH). We also develop a correction for structural constraints on the value of segregation measures, comparable to capacity constraints in a communications channel, that prevent them reaching their theoretical maximum or minimum value.