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    An operator characterizing an extensive measure should pr... — Carmelics
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    Supports→Multiplication is information conserving in the extensive sense, because it preserves only the extensive qualities of numbers (prime factorization), not the order of operands.

    An operator characterizing an extensive measure should preserve only extensive qualities, which multiplication does.

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    Multiplication is information conserving in the extensive sense, because it pres...The information content of a product a×b equals log(a×b) = log a + log b, so δ(a...The order of multiplication is lost (3×4 and 4×3 both yield 12), so multiplicati...

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    Multiplication is information conserving in the extensive sense, becau...73%An extensive property structure entails that lengths share much of the...73%Soundness is an essential requirement of a calculus, while completenes...70%Information efficiency of multiplication is tied to certain algebraic ...69%

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    Multiplication is by definition information conserving. We have: \(\delta(a \times b) = 0\), since \(\log (a \times b) = \log a + \log b\). Still multiplication does not preserve all information in its input: the order of the operation is lost. This is exactly what we want from an operator that characterizes an extensive measure: only the extensive qualities of the numbers are preserved. If we multiply two numbers \(3 \times 4\), then the result, 12, allows us to reconstruct the original computa

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