Absolute value - Revision history

Quidam65: update to more specific category

2021-03-01T23:05:34Z

update to more specific category

DavidB4: removed notice box

2016-04-19T14:56:31Z

removed notice box

GregG: rewrite

2016-04-15T07:08:58Z

rewrite

DavidB4: needs to be improved...commented out statement in question

2016-04-15T01:40:07Z

needs to be improved...commented out statement in question

DavidB4: fixed logic error, though the language sounds a little odd.

2016-04-14T22:35:59Z

fixed logic error, though the language sounds a little odd.

MelH: Correcting error inserted by vandal four years ago.

2015-06-25T02:21:47Z

Correcting error inserted by vandal four years ago.

GregG: complex absolute value is sometimes called modulus

2015-06-25T01:45:04Z

complex absolute value is sometimes called modulus

Karajou: Reverted edits by Sallyburkhalter (talk) to last revision by Aschlafly

2011-11-16T06:16:47Z

Reverted edits by Sallyburkhalter (talk) to last revision by Aschlafly

Sallyburkhalter: Blood, cum, and fecal matter everywhere.) (using Zalgo.py

2011-11-16T06:11:37Z

Blood, cum, and fecal matter everywhere.) (using Zalgo.py

Aschlafly: Reverted edits by Kevinxu (talk) to last revision by UofGuelphStudent

2011-09-17T20:03:46Z

Reverted edits by Kevinxu (talk) to last revision by UofGuelphStudent

← Older revision		Revision as of 23:05, March 1, 2021
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	[[Category:Algebra Terms]]		[[Category:Algebra Terms]]
−	~~[[Category:Algebra]]~~
−	~~[[Category:Mathematics]]~~

← Older revision		Revision as of 14:56, April 19, 2016
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−	<div style="border: 1px solid #c0b8cc; background-color: #f0e5ff; width: 80%; margin: 0 auto 1em auto; padding: .2em; text-align:center">This article or section needs to be rewritten, because:<BR> ''the initial statement of logic is unclear''. ([[talk:{{PAGENAMEE}}\|Discuss]])</div><includeonly>[[category:Articles needing a rewrite]]</includeonly>
−
	'''Absolute value''' is a [[function]] measuring a number's distance from zero. The absolute value of <math>x</math> is written <math>\|x\|</math>.		'''Absolute value''' is a [[function]] measuring a number's distance from zero. The absolute value of <math>x</math> is written <math>\|x\|</math>.

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 <div style="border: 1px solid #c0b8cc; background-color: #f0e5ff; width: 80%; margin: 0 auto 1em auto; padding: .2em; text-align:center">This article or section needs to be rewritten, because:<BR> ''the initial statement of logic is unclear''. ([[talk:{{PAGENAMEE}}|Discuss]])</div><includeonly>[[category:Articles needing a rewrite]]</includeonly>
-The '''absolute value''' of a number is a measure of the size of that number.  The absolute value of <math>x</math> is written <math>|x|</math>.
+'''Absolute value''' is a [[function]] measuring a number's distance from zero.  The absolute value of <math>x</math> is written <math>|x|</math>.
-:If <math>x</math> is a positive number, then <math>|x| = x</math>.
+*If <math>x</math> is a positive number, then <math>|x| = x</math>.
-<!--:If <math>x</math> is a negative number, then <math>|-x| = x</math>. -->
+*If <math>x</math> is a negative number, then <math>|x| = -x</math>.
-:If <math>x=0</math> then <math>|x| = 0</math>.
+*If <math>x=0</math> then <math>|x| = 0</math>.
 Absolute value has several useful properties.  One is the ''multiplicative'' property.  If <math>x</math> and <math>y</math> are two numbers, then <math>|xy| = |x| \times |y|</math>.  Another is the ''triangle inequality'', which is the fact that <math>|x+y| \leq |x| + |y|</math>.  For example, if <math>x = 3</math> and <math>y = -5</math>, then <math>|x+y| = |3 + (-5)| = |3 - 5| = |-2| = 2</math>, while <math>|x| + |y| = |-5| + |3| = 5 + 3 = 8</math>.  In this case, the triangle inequality is the fact that 2 is not more than 8.
 [[Complex number]]s also have an absolute value (sometimes called the modulus).  If <math>z = x+iy</math> is a complex number with real part <math>x</math> and imaginary part <math>y</math>, then <math>|z| = \sqrt{x^2 + y^2}</math>.  If we represent <math>z</math> as a point in the complex plane with coordinates <math>(x,y)</math>, then <math>|z|</math> is the distance from this point to the origin.  The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.

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 The '''absolute value''' of a number is a measure of the size of that number.  The absolute value of <math>x</math> is written <math>|x|</math>.
 :If <math>x</math> is a positive number, then <math>|x| = x</math>.
+<!--:If <math>x</math> is a negative number, then <math>|-x| = x</math>. -->
 :If <math>x=0</math> then <math>|x| = 0</math>.

@@ Line 3: / Line 3: @@
 :If <math>x</math> is a positive number, then <math>|x| = x</math>.
-:If <math>x</math> is a negative number, then <math>|x| = -x</math>.
+:If <math>x</math> is a negative number, then <math>|-x| = x</math>.
 :If <math>x=0</math> then <math>|x| = 0</math>.

@@ Line 9: / Line 9: @@
 Absolute value has several useful properties.  One is the ''multiplicative'' property.  If <math>x</math> and <math>y</math> are two numbers, then <math>|xy| = |x| \times |y|</math>.  Another is the ''triangle inequality'', which is the fact that <math>|x+y| \leq |x| + |y|</math>.  For example, if <math>x = 3</math> and <math>y = -5</math>, then <math>|x+y| = |3 + (-5)| = |3 - 5| = |-2| = 2</math>, while <math>|x| + |y| = |-5| + |3| = 5 + 3 = 8</math>.  In this case, the triangle inequality is the fact that 2 is not more than 8.
-[[Complex number]]s also have an absolute value.  If <math>z = x+iy</math> is a complex number with real part <math>x</math> and imaginary part <math>y</math>, then <math>|z| = \sqrt{x^2 + y^2}</math>.  If we represent <math>z</math> as a point in the complex plane with coordinates <math>(x,y)</math>, then <math>|z|</math> is the distance from this point to the origin.  The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.
+[[Complex number]]s also have an absolute value (sometimes called the modulus).  If <math>z = x+iy</math> is a complex number with real part <math>x</math> and imaginary part <math>y</math>, then <math>|z| = \sqrt{x^2 + y^2}</math>.  If we represent <math>z</math> as a point in the complex plane with coordinates <math>(x,y)</math>, then <math>|z|</math> is the distance from this point to the origin.  The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.
 [[Category:Algebra Terms]]
 [[Category:Algebra]]
 [[Category:Mathematics]]

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−	~~</pre>~~
	The '''absolute value''' of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>\|x\|</math>.		The '''absolute value''' of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>\|x\|</math>.

← Older revision		Revision as of 06:11, November 16, 2011
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		+	</pre>
	The '''absolute value''' of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>\|x\|</math>.		The '''absolute value''' of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>\|x\|</math>.