Undirected value: Difference between revisions

Cmloegcmluin (talk | contribs)
Formula: hone connotations
Cmloegcmluin (talk | contribs)
Analogies: fix formatting of formula
 
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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>.
=== Using a base ===
For the positives only (<math>x > 0</math>), we find an identity using logarithms and exponentiation:
<math>
\overline{\underline{x} = b^{|log_b(x)|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\
</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.
And a '''unison''' number is a real number whose absolute value is equal to 1 (that is, it is either 1 or -1).


{| class="wikitable"
{| class="wikitable"
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|-
|-
!unsigned
!unsigned
|
|<math>\infty</math>
|n/a
|n/a
|0
|0
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|<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 ==