Undirected value: Difference between revisions
Cmloegcmluin (talk | contribs) →Formula: hone connotations |
Sintel bot (talk | contribs) Fix <math> environments for MathJax v4 (align->aligned, etc.) |
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<math> | <math> | ||
\overline{\underline{x}} = | \overline{\underline{x}} = | ||
\begin{cases} | \begin{cases} | ||
x & \text{if} \; |x| \ge 1 \\ | x & \text{if} \; |x| \ge 1 \\ | ||
\frac{1}{x} & \text{if} \; |x| < 1 \\ | \frac{1}{x} & \text{if} \; |x| < 1 \\ | ||
\end{cases} | \end{cases} | ||
</math> | </math> | ||
| Line 76: | Line 74: | ||
To be clear, if the input is not already in ratio form, for example <math>\phi</math>, this formula requires it first to be placed over 1, like <math>\frac{\phi}{1}</math>. | To be clear, if the input is not already in ratio form, for example <math>\phi</math>, this formula requires it first to be placed over 1, like <math>\frac{\phi}{1}</math>. | ||
== Superunison, subunison, and unison numbers == | == Superunison, subunison, and unison numbers == | ||
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A '''subunison''' number, by extension, is a real number whose absolute value is less than 1. | A '''subunison''' number, by extension, is a real number whose absolute value is less than 1. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 107: | Line 94: | ||
|- | |- | ||
!unsigned | !unsigned | ||
| | |<math>\infty</math> | ||
|n/a | |n/a | ||
|0 | |0 | ||
| Line 185: | Line 172: | ||
|<math>\overline{\underline{x}}</math> | |<math>\overline{\underline{x}}</math> | ||
|} | |} | ||
The following identity shows the relationship between the undirected value and the absolute value, for positive real numbers. | |||
<math> | |||
\overline{\underline{x}} = b^{|log_{b}{x}|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\ | |||
</math> | |||
== Graphs == | == Graphs == | ||