Height: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 448206562 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 448319040 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-09-03 14:26:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>448319040</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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[[math]] | [[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. An example would be octave-equivalence, where two ratios p and q are considered equivalent if the following is true: | 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]] | [[math]] | ||
2^{-v_2 \left( {p} \right)} p = 2^{-v_2 \left( {q} \right)} q | 2^{-v_2 \left( {p} \right)} p = 2^{-v_2 \left( {q} \right)} q | ||
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--><script type="math/tex">H \left( {q} \right) \equiv F \left( {H} \left( {q} \right) \right)</script><!-- ws:end:WikiTextMathRule:0 --><br /> | --><script type="math/tex">H \left( {q} \right) \equiv F \left( {H} \left( {q} \right) \right)</script><!-- ws:end:WikiTextMathRule:0 --><br /> | ||
<br /> | <br /> | ||
A <strong>semi-height</strong> 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. An example would be octave-equivalence, where two ratios p and q are considered equivalent if the following is true:<br /> | A <strong>semi-height</strong> 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:<br /> | ||
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[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||