Why is it called commutative property?
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I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets).
Associative because when the same associative operator appear in a row, you can change around the numbers.
But why is the commutative property called commutative?
definition math-history
edited 35 mins ago
Eevee Trainer
3,355225
asked 55 mins ago
Jay Patel
213
add a comment |
up vote
1
down vote
favorite
I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets).
Associative because when the same associative operator appear in a row, you can change around the numbers.
But why is the commutative property called commutative?
definition math-history
edited 35 mins ago
Eevee Trainer
3,355225
asked 55 mins ago
Jay Patel
213
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets).
Associative because when the same associative operator appear in a row, you can change around the numbers.
But why is the commutative property called commutative?
definition math-history
edited 35 mins ago
Eevee Trainer
3,355225
asked 55 mins ago
Jay Patel
213
I can see why distributive is called distributive (distribute whatever you are multiplying to everything within the brackets).
Associative because when the same associative operator appear in a row, you can change around the numbers.
But why is the commutative property called commutative?
definition math-history
definition math-history
edited 35 mins ago
Eevee Trainer
3,355225
asked 55 mins ago
Jay Patel
213
edited 35 mins ago
Eevee Trainer
3,355225
asked 55 mins ago
Jay Patel
213
edited 35 mins ago
Eevee Trainer
3,355225
edited 35 mins ago
Eevee Trainer
3,355225
edited 35 mins ago
Eevee Trainer
3,355225
3,355225
asked 55 mins ago
Jay Patel
213
asked 55 mins ago
Jay Patel
213
asked 55 mins ago
Jay Patel
213
213
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago
add a comment |
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago
add a comment |
3 Answers
3
active
oldest
votes
up vote
4
down vote
From the Wikipedia article "Commutative Property", under History and Etymology:
The first recorded use of the term commutative was in a memoir by François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in 1838 in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.
answered 53 mins ago
Dane
2,9851533
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
add a comment |
up vote
3
down vote
https://www.merriam-webster.com/dictionary/commutative
https://www.merriam-webster.com/dictionary/commutation
Commutative, from commutation, which means exchange, trade, or replacement according to the first 2 definitions. The commutative property says that the order in which the operation is carried out does not matter. You can exchange/trace factors or addends and still arrive at the same product or sum.
https://www.thefreedictionary.com/commutative
Definition one of the adjective form gives "involving substitution, interchange"
So you just switch or commute the two addends or factors and get the same sum or product!
answered 50 mins ago
Christopher Marley
935115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
add a comment |
up vote
0
down vote
Seems pretty reasonable since commute means to move around or change places, approximately. One of the most basic ways of moving elements around is to switch their order.
I guess another word could have been used. Of course "abelian" is used for groups, after Niels Henrik Abel.
answered 30 mins ago
Chris Custer
10.3k3724
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
From the Wikipedia article "Commutative Property", under History and Etymology:
The first recorded use of the term commutative was in a memoir by François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in 1838 in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.
answered 53 mins ago
Dane
2,9851533
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
add a comment |
up vote
4
down vote
From the Wikipedia article "Commutative Property", under History and Etymology:
The first recorded use of the term commutative was in a memoir by François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in 1838 in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.
answered 53 mins ago
Dane
2,9851533
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
add a comment |
up vote
4
down vote
up vote
4
down vote
From the Wikipedia article "Commutative Property", under History and Etymology:
The first recorded use of the term commutative was in a memoir by François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in 1838 in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.
answered 53 mins ago
Dane
2,9851533
From the Wikipedia article "Commutative Property", under History and Etymology:
The first recorded use of the term commutative was in a memoir by François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in 1838 in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.
answered 53 mins ago
Dane
2,9851533
answered 53 mins ago
Dane
2,9851533
answered 53 mins ago
Dane
2,9851533
answered 53 mins ago
Dane
2,9851533
2,9851533
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
add a comment |
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
1
1
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
47 mins ago
add a comment |
up vote
3
down vote
https://www.merriam-webster.com/dictionary/commutative
https://www.merriam-webster.com/dictionary/commutation
Commutative, from commutation, which means exchange, trade, or replacement according to the first 2 definitions. The commutative property says that the order in which the operation is carried out does not matter. You can exchange/trace factors or addends and still arrive at the same product or sum.
https://www.thefreedictionary.com/commutative
Definition one of the adjective form gives "involving substitution, interchange"
So you just switch or commute the two addends or factors and get the same sum or product!
answered 50 mins ago
Christopher Marley
935115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
add a comment |
up vote
3
down vote
https://www.merriam-webster.com/dictionary/commutative
https://www.merriam-webster.com/dictionary/commutation
Commutative, from commutation, which means exchange, trade, or replacement according to the first 2 definitions. The commutative property says that the order in which the operation is carried out does not matter. You can exchange/trace factors or addends and still arrive at the same product or sum.
https://www.thefreedictionary.com/commutative
Definition one of the adjective form gives "involving substitution, interchange"
So you just switch or commute the two addends or factors and get the same sum or product!
answered 50 mins ago
Christopher Marley
935115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
add a comment |
up vote
3
down vote
up vote
3
down vote
https://www.merriam-webster.com/dictionary/commutative
https://www.merriam-webster.com/dictionary/commutation
Commutative, from commutation, which means exchange, trade, or replacement according to the first 2 definitions. The commutative property says that the order in which the operation is carried out does not matter. You can exchange/trace factors or addends and still arrive at the same product or sum.
https://www.thefreedictionary.com/commutative
Definition one of the adjective form gives "involving substitution, interchange"
So you just switch or commute the two addends or factors and get the same sum or product!
answered 50 mins ago
Christopher Marley
935115
https://www.merriam-webster.com/dictionary/commutative
https://www.merriam-webster.com/dictionary/commutation
Commutative, from commutation, which means exchange, trade, or replacement according to the first 2 definitions. The commutative property says that the order in which the operation is carried out does not matter. You can exchange/trace factors or addends and still arrive at the same product or sum.
https://www.thefreedictionary.com/commutative
Definition one of the adjective form gives "involving substitution, interchange"
So you just switch or commute the two addends or factors and get the same sum or product!
answered 50 mins ago
Christopher Marley
935115
answered 50 mins ago
Christopher Marley
935115
answered 50 mins ago
Christopher Marley
935115
answered 50 mins ago
Christopher Marley
935115
935115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
add a comment |
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
32 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
I see the word in legal context, " a death sentence has been commuted to life imprisonment". Looks like here also it means replacement.
– P Vanchinathan
30 mins ago
add a comment |
up vote
0
down vote
Seems pretty reasonable since commute means to move around or change places, approximately. One of the most basic ways of moving elements around is to switch their order.
I guess another word could have been used. Of course "abelian" is used for groups, after Niels Henrik Abel.
answered 30 mins ago
Chris Custer
10.3k3724
add a comment |
up vote
0
down vote
Seems pretty reasonable since commute means to move around or change places, approximately. One of the most basic ways of moving elements around is to switch their order.
I guess another word could have been used. Of course "abelian" is used for groups, after Niels Henrik Abel.
answered 30 mins ago
Chris Custer
10.3k3724
add a comment |
up vote
0
down vote
up vote
0
down vote
Seems pretty reasonable since commute means to move around or change places, approximately. One of the most basic ways of moving elements around is to switch their order.
I guess another word could have been used. Of course "abelian" is used for groups, after Niels Henrik Abel.
answered 30 mins ago
Chris Custer
10.3k3724
Seems pretty reasonable since commute means to move around or change places, approximately. One of the most basic ways of moving elements around is to switch their order.
I guess another word could have been used. Of course "abelian" is used for groups, after Niels Henrik Abel.
answered 30 mins ago
Chris Custer
10.3k3724
answered 30 mins ago
Chris Custer
10.3k3724
answered 30 mins ago
Chris Custer
10.3k3724
answered 30 mins ago
Chris Custer
10.3k3724
10.3k3724
add a comment |
add a comment |
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I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
49 mins ago