Height: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 12:17:10 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 12:18:14 UTC</tt>.<br>

: The original revision id was <tt>~~363458620~~</tt>.<br>

: The original revision id was <tt>363459326</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>

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[[math]]

An **Improper ~~Height~~** is a function which does not obey criteria #1 above in the strictest sense, 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:

An **Improper height** is a function which does not obey criteria #1 above in the strictest sense, 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:

[[math]]

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><br />

<br />

An <strong>Improper ~~Height~~</strong> is a function which does not obey criteria #1 above in the strictest sense, 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 />

An <strong>Improper height</strong> is a function which does not obey criteria #1 above in the strictest sense, 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 />

<!-- ws:start:WikiTextMathRule:1:

[[math]]&lt;br/&gt;

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 12:17:10 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 12:18:14 UTC</tt>.<br>
-: The original revision id was <tt>363458620</tt>.<br>
+: The original revision id was <tt>363459326</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>
@@ Line 20: / Line 20: @@
 [[math]]
-An **Improper Height** is a function which does not obey criteria #1 above in the strictest sense, 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:
+An **Improper height** is a function which does not obey criteria #1 above in the strictest sense, 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:
 [[math]]
 ^{-v_2 \left( {p} \right)} p = 2^{-v_2 \left( {q} \right)} q
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   --&gt;&lt;script type="math/tex"&gt;H \left( {q} \right) \equiv F \left( {H} \left( {q} \right) \right)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-An &lt;strong&gt;Improper Height&lt;/strong&gt; is a function which does not obey criteria #1 above in the strictest sense, 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:&lt;br /&gt;
+An &lt;strong&gt;Improper height&lt;/strong&gt; is a function which does not obey criteria #1 above in the strictest sense, 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:&lt;br /&gt;
 &lt;!-- ws:start:WikiTextMathRule:1:
 [[math]]&amp;lt;br/&amp;gt;