Epimorphic scale: Difference between revisions
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Define <math>v:A \to \mathbb{Z}</math> by defining <math>v(\mathbf{s}) = 1</math> for any step <math>\mathbf{s} \in C_1</math> and extending uniquely by linearity. Then for any <math>i \in \mathbb{Z}</math> we have <math>v(S[i]) = v(S[i]/S[i-1]\cdots S[1]) = v(S[i]/S[i-1]) + \cdots + v(S[1]) = i.</math> That <math>v(2) = n</math> is also automatic. | Define the val <math>v:A \to \mathbb{Z}</math> by defining <math>v(\mathbf{s}) = 1</math> for any step <math>\mathbf{s} \in C_1</math> and extending uniquely by linearity. Then for any <math>i \in \mathbb{Z}</math> we have <math>v(S[i]) = v(S[i]/S[i-1]\cdots S[1]) = v(S[i]/S[i-1]) + \cdots + v(S[1]) = i.</math> That <math>v(2) = n</math> is also automatic. | ||
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[[Category:Scale]] | [[Category:Scale]] | ||