User:Inthar/Epimorphic temperament: Difference between revisions

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 === Epimorphic scales are CS ===
 {{proof|contents=
-Let <math>x \in C_j</math> where without loss of generality ''j'' > 0. Then there exists <math>i > 0</math> such that <math>S[i+j]/S[i] = x.</math> Suppose by way of contradiction there exist <math>k > 0, k \neq j</math> and <math>i > 0</math> such that <math>S[i+k]/S[i] = x.</math>
+Let <math>x \in C_j.</math> Then there exists <math>i > 0</math> such that <math>S[i+j]/S[i] = x.</math> Suppose by way of contradiction there exist <math>k \neq j</math> and <math>i > 0</math> such that <math>S[i+k]/S[i] = x.</math>
 Then <math>v(x) = v(S[i+j]/S[i]) = v(S[i+j]) - v(S[i]) = i+k - i = j,</math> but also <math>v(x) = v(S[i^\prime+k]/S[i^\prime]) = v(S[i^\prime+k]) - v(S[i^\prime]) = k,</math> a contradiction.