Talk:2028: Complex Numbers - Revision history

Qwertyuiopfromdefly: commented again

2026-02-17T03:34:11Z

commented again

82.132.239.46 at 11:30, 16 February 2026

2026-02-16T11:30:39Z

Qwertyuiopfromdefly: fixed typos in previous comment

2026-02-16T04:20:21Z

fixed typos in previous comment

Qwertyuiopfromdefly: commented

2026-02-16T04:19:28Z

commented

SteveBaker: Floating point arrays.

2020-07-06T16:00:04Z

Floating point arrays.

162.158.134.112 at 13:48, 9 August 2018

2018-08-09T13:48:24Z

162.158.75.130 at 18:17, 7 August 2018

2018-08-07T18:17:23Z

Jeremyp at 10:26, 6 August 2018

2018-08-06T10:26:06Z

108.162.215.160: half the operations gets you half a group.

2018-08-05T09:40:12Z

half the operations gets you half a group.

162.158.90.6 at 09:59, 4 August 2018

2018-08-04T09:59:47Z

← Older revision		Revision as of 03:34, 17 February 2026
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	:Ironically, because of the traditional "disproportionately big head on a child" look being subverted in xkcd (adults have proportionately larger head-to-body ratios), this desk-sitter's proportions look like adult Cueball more than Kidball, even without other possible scale-cues being available.		:Ironically, because of the traditional "disproportionately big head on a child" look being subverted in xkcd (adults have proportionately larger head-to-body ratios), this desk-sitter's proportions look like adult Cueball more than Kidball, even without other possible scale-cues being available.
	:Might be fodder for a "Student(s) And Teacher"-type super-category, though, if there was sufficient need for one. There are a number of these comics, whether or not consensus would agree with yet another new Cat. [[Special:Contributions/82.132.239.46\|82.132.239.46]] 11:30, 16 February 2026 (UTC)		:Might be fodder for a "Student(s) And Teacher"-type super-category, though, if there was sufficient need for one. There are a number of these comics, whether or not consensus would agree with yet another new Cat. [[Special:Contributions/82.132.239.46\|82.132.239.46]] 11:30, 16 February 2026 (UTC)
		+	:: Okay sorry. [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 03:34, 17 February 2026 (UTC)

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	I believe that the character here is [[Kidball]], feel free to correct me. [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 04:19, 16 February 2026 (UTC)		I believe that the character here is [[Kidball]], feel free to correct me. [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 04:19, 16 February 2026 (UTC)
		+	:Sorry, but I just did. There's no reason to believe this student is a child. Height-wise, he'd be taller than his teacher (which is not to say that ''I'' didn't have female teachers who became smaller than me, even during early adolescence), assuming no different level of 'zoom' applied to the respective panels, and though I first seriously encountered complex numbers maybe in the mid-teens (from school... my Dad probably introduced me to them earlier, because we were like that, but not in a practical or even academically thorough way), the more philosophical and in-depth aspects of the lesson seem to suggest more university-age lessons that would feature 'young adults' (and outright 'mature students') who may be comparatively young but aren't children.
		+	:Ironically, because of the traditional "disproportionately big head on a child" look being subverted in xkcd (adults have proportionately larger head-to-body ratios), this desk-sitter's proportions look like adult Cueball more than Kidball, even without other possible scale-cues being available.
		+	:Might be fodder for a "Student(s) And Teacher"-type super-category, though, if there was sufficient need for one. There are a number of these comics, whether or not consensus would agree with yet another new Cat. [[Special:Contributions/82.132.239.46\|82.132.239.46]] 11:30, 16 February 2026 (UTC)

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	"Does any of this really have to do with vectors? Or do mathematicians just think they're too cool for regular floating point arrays? [[User:SteveBaker\|SteveBaker]] ([[User talk:SteveBaker\|talk]]) 16:00, 6 July 2020 (UTC)		"Does any of this really have to do with vectors? Or do mathematicians just think they're too cool for regular floating point arrays? [[User:SteveBaker\|SteveBaker]] ([[User talk:SteveBaker\|talk]]) 16:00, 6 July 2020 (UTC)

−	I believe that the character here is [[Kidball]] feel free to correct me [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 04:19, 16 February 2026 (UTC)	+	I believe that the character here is [[Kidball]], feel free to correct me. [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 04:19, 16 February 2026 (UTC)

← Older revision		Revision as of 04:19, 16 February 2026
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	"Does any of this really have to do with vectors? Or do mathematicians just think they're too cool for regular floating point arrays? [[User:SteveBaker\|SteveBaker]] ([[User talk:SteveBaker\|talk]]) 16:00, 6 July 2020 (UTC)		"Does any of this really have to do with vectors? Or do mathematicians just think they're too cool for regular floating point arrays? [[User:SteveBaker\|SteveBaker]] ([[User talk:SteveBaker\|talk]]) 16:00, 6 July 2020 (UTC)
		+
		+	I believe that the character here is [[Kidball]] feel free to correct me [[User:Qwertyuiopfromdefly\|Qwertyuiopfromdefly]] ([[User talk:Qwertyuiopfromdefly\|talk]]) 04:19, 16 February 2026 (UTC)

← Older revision		Revision as of 16:00, 6 July 2020
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	Real numbers with regular multiplication is not a group, as zero does not have an inverse element. The example would work with addition --[[Special:Contributions/162.158.134.112\|162.158.134.112]] 13:48, 9 August 2018 (UTC)Random guy who read the article		Real numbers with regular multiplication is not a group, as zero does not have an inverse element. The example would work with addition --[[Special:Contributions/162.158.134.112\|162.158.134.112]] 13:48, 9 August 2018 (UTC)Random guy who read the article
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		+
		+	"Does any of this really have to do with vectors? Or do mathematicians just think they're too cool for regular floating point arrays? [[User:SteveBaker\|SteveBaker]] ([[User talk:SteveBaker\|talk]]) 16:00, 6 July 2020 (UTC)

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	Shouldn't the description of a group involve ''two'' operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a {{w\|semigroup}}.[[Special:Contributions/108.162.215.160\|108.162.215.160]] 09:40, 5 August 2018 (UTC)		Shouldn't the description of a group involve ''two'' operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a {{w\|semigroup}}.[[Special:Contributions/108.162.215.160\|108.162.215.160]] 09:40, 5 August 2018 (UTC)
	: No. The inverse operation arises as a consequence of the fact that it's a group. A group satisfies four conditions: 1. it is closed under the operation, 2. the operation is associative 3. there is an identity e such that a op e = e op a = a. 4. For every element a, there is a unique element b such that a op b = b op a = e. The inverse function falls out as a result of conditions 3 and 4 [[User:Jeremyp\|Jeremyp]] ([[User talk:Jeremyp\|talk]]) 10:26, 6 August 2018 (UTC)		: No. The inverse operation arises as a consequence of the fact that it's a group. A group satisfies four conditions: 1. it is closed under the operation, 2. the operation is associative 3. there is an identity e such that a op e = e op a = a. 4. For every element a, there is a unique element b such that a op b = b op a = e. The inverse function falls out as a result of conditions 3 and 4 [[User:Jeremyp\|Jeremyp]] ([[User talk:Jeremyp\|talk]]) 10:26, 6 August 2018 (UTC)
		+
		+	Real numbers with regular multiplication is not a group, as zero does not have an inverse element. The example would work with addition --[[Special:Contributions/162.158.134.112\|162.158.134.112]] 13:48, 9 August 2018 (UTC)Random guy who read the article

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	It's a false dilemma. Complex numbers ''are'' vectors (<math>\mathbb{C}</math> is a two-dimensional <math>\mathbb{R}</math>-vector space, and more generally every field is a vector space over any subfield), but that doesn't change anything about the fact that <math>i</math> is by definition a square root of -1. [[User:Zmatt\|Zmatt]] ([[User talk:Zmatt\|talk]]) 20:38, 3 August 2018 (UTC)		It's a false dilemma. Complex numbers ''are'' vectors (<math>\mathbb{C}</math> is a two-dimensional <math>\mathbb{R}</math>-vector space, and more generally every field is a vector space over any subfield), but that doesn't change anything about the fact that <math>i</math> is by definition a square root of -1. [[User:Zmatt\|Zmatt]] ([[User talk:Zmatt\|talk]]) 20:38, 3 August 2018 (UTC)
		+
		+	Important concepts in math usually show up naturally in many apparently unrelated areas. Each area will name and define a concept that makes sense for the problems being considered. One of the joys of math is proving that multiple, apparently unrelated, definitions are equivalent. When definitions are equivalent you cannot pick "the one true definition" -- any of them will do. However the principle of maximum laziness leads to the one with the easiest notion being used as a canonical definition.[[Special:Contributions/162.158.75.130\|162.158.75.130]] 18:17, 7 August 2018 (UTC)

	Fun factoid: not only is <math>\mathbb{C}</math> the unique proper field extension of finite degree over <math>\mathbb{R}</math> (since <math>\mathbb{C}</math> is algebraically closed), but the converse is true as well: <math>\mathbb{R}</math> is the only proper subfield of finite index in <math>\mathbb{C}</math>. They're like a weird married couple. [[User:Zmatt\|Zmatt]] ([[User talk:Zmatt\|talk]]) 20:53, 3 August 2018 (UTC)		Fun factoid: not only is <math>\mathbb{C}</math> the unique proper field extension of finite degree over <math>\mathbb{R}</math> (since <math>\mathbb{C}</math> is algebraically closed), but the converse is true as well: <math>\mathbb{R}</math> is the only proper subfield of finite index in <math>\mathbb{C}</math>. They're like a weird married couple. [[User:Zmatt\|Zmatt]] ([[User talk:Zmatt\|talk]]) 20:53, 3 August 2018 (UTC)

← Older revision		Revision as of 10:26, 6 August 2018
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	Shouldn't the description of a group involve ''two'' operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a {{w\|semigroup}}.[[Special:Contributions/108.162.215.160\|108.162.215.160]] 09:40, 5 August 2018 (UTC)		Shouldn't the description of a group involve ''two'' operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a {{w\|semigroup}}.[[Special:Contributions/108.162.215.160\|108.162.215.160]] 09:40, 5 August 2018 (UTC)
		+	: No. The inverse operation arises as a consequence of the fact that it's a group. A group satisfies four conditions: 1. it is closed under the operation, 2. the operation is associative 3. there is an identity e such that a op e = e op a = a. 4. For every element a, there is a unique element b such that a op b = b op a = e. The inverse function falls out as a result of conditions 3 and 4 [[User:Jeremyp\|Jeremyp]] ([[User talk:Jeremyp\|talk]]) 10:26, 6 August 2018 (UTC)

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	:One should note that the concept of complex numbers actually is older than vector spaces. So while it is true that complex numbers are a cool variant of vectors, historically that's not true, because vectors were more or less unknown when complex numbers were used for the first time. --[[Special:Contributions/162.158.90.6\|162.158.90.6]] 09:59, 4 August 2018 (UTC)		:One should note that the concept of complex numbers actually is older than vector spaces. So while it is true that complex numbers are a cool variant of vectors, historically that's not true, because vectors were more or less unknown when complex numbers were used for the first time. --[[Special:Contributions/162.158.90.6\|162.158.90.6]] 09:59, 4 August 2018 (UTC)
		+
		+	Shouldn't the description of a group involve ''two'' operations? There is a binary operation that gloms two things together to make a new thing, but there's also a unary operation that takes only one thing and makes a new thing -- the inverse. Without the unary operation, you only have a {{w\|semigroup}}.[[Special:Contributions/108.162.215.160\|108.162.215.160]] 09:40, 5 August 2018 (UTC)

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	Altho there are no "meta-abelian" groups there are metabelian groups. If xy=yx then the commutator [x,y]=xyx^{-1}y^{-1}=1. The group generated by the commutators -- the commutator subgroup -- is thus a measure of how far a group is from being abelian. A metabelian group is a nonabelian group whose commutator subgroup is abelian. Thus a metabelian group is one made of a stack of two abelian groups. It is "meta-abelian" in that sense. A standard example is the group of invertible upper-trianglular matrices. The commutators all have 1s on the diagonals.		Altho there are no "meta-abelian" groups there are metabelian groups. If xy=yx then the commutator [x,y]=xyx^{-1}y^{-1}=1. The group generated by the commutators -- the commutator subgroup -- is thus a measure of how far a group is from being abelian. A metabelian group is a nonabelian group whose commutator subgroup is abelian. Thus a metabelian group is one made of a stack of two abelian groups. It is "meta-abelian" in that sense. A standard example is the group of invertible upper-trianglular matrices. The commutators all have 1s on the diagonals.
		+
		+	:One should note that the concept of complex numbers actually is older than vector spaces. So while it is true that complex numbers are a cool variant of vectors, historically that's not true, because vectors were more or less unknown when complex numbers were used for the first time. --[[Special:Contributions/162.158.90.6\|162.158.90.6]] 09:59, 4 August 2018 (UTC)