Undirected value - Revision history

Cmloegcmluin: /* Analogies */ fix formatting of formula

2022-04-17T18:06:49Z

Analogies: fix formatting of formula

← Older revision		Revision as of 18:06, 17 April 2022
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	<math>		<math>
	\overline{\underline{x} = b^{\|~~log_b(~~x)\|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\		\overline{\underline{x}} = b^{\|log_{b}{x}\|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\
	</math>		</math>


	== Graphs ==		== Graphs ==

2022-04-17T18:03:29Z

Superunison, subunison, and unison numbers: remove incorrect statement about unison

← Older revision		Revision as of 18:03, 17 April 2022
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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

2022-04-17T00:20:10Z

better home for that identity

@@ Line 76: / Line 76: @@
 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 ==
@@ Line 185: / Line 176: @@
 |<math>\overline{\underline{x}}</math>
 |}
 == Graphs ==

2022-04-17T00:16:24Z

Formula: hone connotations

← Older revision		Revision as of 00:16, 17 April 2022
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	This alternative is designed to evoke the infix ":" 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.

	==~~Formula~~==		==Definitions==

	=== As real ===		=== As real ===
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	=== Using a base ===		=== Using a base ===

	For the positives only (<math>x > 0</math>), we ~~have another way to define the undirected value,~~ using logarithms and exponentiation:		For the positives only (<math>x > 0</math>), we find an identity using logarithms and exponentiation:

2022-04-17T00:15:13Z

Using a base: fix typos

← Older revision		Revision as of 00:15, 17 April 2022
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	<math>		<math>
	\overline{\underline{~~\frac{n}{d}}~~} = b^{log_b(x)} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\		\overline{\underline{x} = b^{\|log_b(x)\|} \;\; \text{for any base} \; b>1 \; \text{and} \; x>0 \\
	</math>		</math>

2022-04-17T00:09:11Z

Superunison, subunison, and unison numbers: improve table

2022-04-15T15:43:45Z

add graphs

← Older revision		Revision as of 15:43, 15 April 2022
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	\|}		\|}

			== 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 ==

2022-04-15T15:30:48Z

Formula: add another formula

← Older revision		Revision as of 15:30, 15 April 2022
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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 have another way to define the undirected value, using logarithms and exponentiation:


			<math>
			\overline{\underline{\frac{n}{d}}} = 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 ==

2022-04-15T15:23:14Z

Alternative: typo, correction, clarification, and preference showcase

← Older revision		Revision as of 15:23, 15 April 2022
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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, a alternative mathematical notation is suggested: the value may be ~~both infixed and~~ outfixed with colons, as in ":x:".		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.

	==Formula==		==Formula==

2022-04-15T15:05:38Z

Superunison, subunison, and unison numbers: correction to table