Undirected value: Difference between revisions
Cmloegcmluin (talk | contribs) simpler and clearer way to put this |
Cmloegcmluin (talk | contribs) →Analogies: fix formatting of formula |
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==== Alternative ==== | ==== Alternative ==== | ||
In situations where it is difficult to realize either the <math>\LaTeX</math> or Unicode formats, and the function notation is not desired for some reason, | In situations where it is difficult to realize either the <math>\LaTeX</math> or Unicode formats, and the function notation is not desired for some reason, an alternative mathematical notation is suggested: the value may be outfixed with colons, as in ":x:". | ||
For example, :4/5: = 5/4. | For example, :4/5: = 4:5 = 5/4. | ||
This alternative is designed to evoke the ":" operator which as previously described is the one typically used for undirected ratios. | This alternative is designed to evoke the infix ":" operator which as previously described is the one typically used for undirected ratios. | ||
== | ==Definitions== | ||
=== As real === | === As real === | ||
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<math> | <math> | ||
\overline{\underline{\frac{n}{d}}} = \text{sign}(\frac{n}{d})\frac{\ | \overline{\underline{\frac{n}{d}}} = \text{sign}(\frac{n}{d})\frac{\max(|n|, |d|)}{\min(|n|, |d|)} | ||
</math> | </math> | ||
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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" | ||
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! | ! | ||
!superunison | !superunison | ||
! | !undirected | ||
!subunison | !subunison | ||
|- | |- | ||
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|<math>\frac12</math> | |<math>\frac12</math> | ||
|- | |- | ||
! | !unsigned | ||
|<math>\infty</math> | |||
|n/a | |||
|0 | |0 | ||
|- | |- | ||
!negative | !negative | ||
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|} | |} | ||
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 == | |||
[[File:Und x.png|300px|frame|left|plot of the undirected value of x]] | |||
[[File:Abs x.png|300px|frame|left|plot of the absolute value of x, for comparison]] | |||
<br clear=all> | |||
== History == | == History == | ||