Height: Difference between revisions
→Examples of Height Functions:: simplified wiki markup corrected spelling of height in linked articles |
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<math>H \left( {q} \right) \equiv F \left( {H} \left( {q} \right) \right)</math> | <math>H \left( {q} \right) \equiv F \left( {H} \left( {q} \right) \right)</math> | ||
A '''semi-height''' is a function which does not obey criterion #3 above, so that there is a rational number q ≠ 1 such that H(q) = H(1), resulting in an equivalence relation on its elements, under which #1 is modified to a finite number of equivalence classes. An example would be octave | A '''semi-height''' is a function which does not obey criterion #3 above, so that there is a rational number q ≠ 1 such that H(q) = H(1), resulting in an equivalence relation on its elements, under which #1 is modified to a finite number of equivalence classes. An example would be [[octave equivalence]], where two ratios p and q are considered equivalent if the following is true: | ||
<math>2^{-v_2 \left( {p} \right)} p = 2^{-v_2 \left( {q} \right)} q</math> | <math>2^{-v_2 \left( {p} \right)} p = 2^{-v_2 \left( {q} \right)} q</math> | ||