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Shannon's entropy and other entropy-based concepts are derived from the new,more general concept of relative divergence of one "grading' function on alinearly ordered set from another such function. The definition of relativedivergence is derived based on "common sense' assumptions about comparinggrading functions. Shannon's entropy formulas emerge from the respectiverelative divergence ones, entropy based methods are extended to more generalcases and some new applications.

Axiomatic Origins of Mathematical Entropy: Grading Ordered Sets