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Does the process of mapping a random range, for example, [4; 55] to [0; 1] have a name? Maybe it's called normalization?

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Yes, I would call it "normalization". You could also call it "scaling" or "rescaling".

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Interesting. After reading "normalization" I agree... but another thing that came to mind was "transformation" because the mapping function could be considered a transformation. Do you agree? – Tom Feb 4 '12 at 16:49
@Tom: Certainly it could be considered a transformation, but that's a lot more general than "normalization". "Transformation" is basically a synonym for "mapping", which occurred in the question, but the question was about a specific kind of mapping. – joriki Feb 5 '12 at 6:54

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