Why is it called commutative property?
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?
terminology definition math-history
edited Dec 19 at 12:42
J W
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
add a comment |
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?
terminology definition math-history
edited Dec 19 at 12:42
J W
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
2
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
1
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28
add a comment |
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?
terminology definition math-history
edited Dec 19 at 12:42
J W
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
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?
terminology definition math-history
terminology definition math-history
edited Dec 19 at 12:42
J W
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
edited Dec 19 at 12:42
J W
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
edited Dec 19 at 12:42
J W
1,8101425
edited Dec 19 at 12:42
J W
1,8101425
edited Dec 19 at 12:42
J W
1,8101425
1,8101425
asked Dec 19 at 2:42
Jay Patel
656
asked Dec 19 at 2:42
Jay Patel
656
asked Dec 19 at 2:42
Jay Patel
656
656
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
2
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
1
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28
add a comment |
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
2
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
1
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
2
2
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
1
1
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28
add a comment |
3 Answers
3
active
oldest
votes
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 Dec 19 at 2:44
Dane
3,1501634
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
add a comment |
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 Dec 19 at 2:47
Christopher Marley
985115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
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
Dec 19 at 3:07
add a comment |
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 Dec 19 at 3:07
Chris Custer
10.5k3724
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045924%2fwhy-is-it-called-commutative-property%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 Dec 19 at 2:44
Dane
3,1501634
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
add a comment |
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 Dec 19 at 2:44
Dane
3,1501634
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
add a comment |
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 Dec 19 at 2:44
Dane
3,1501634
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 Dec 19 at 2:44
Dane
3,1501634
answered Dec 19 at 2:44
Dane
3,1501634
answered Dec 19 at 2:44
Dane
3,1501634
answered Dec 19 at 2:44
Dane
3,1501634
3,1501634
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
add a comment |
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
10
10
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
– Christopher Marley
Dec 19 at 2:50
add a comment |
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 Dec 19 at 2:47
Christopher Marley
985115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
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
Dec 19 at 3:07
add a comment |
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 Dec 19 at 2:47
Christopher Marley
985115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
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
Dec 19 at 3:07
add a comment |
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 Dec 19 at 2:47
Christopher Marley
985115
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 Dec 19 at 2:47
Christopher Marley
985115
answered Dec 19 at 2:47
Christopher Marley
985115
answered Dec 19 at 2:47
Christopher Marley
985115
answered Dec 19 at 2:47
Christopher Marley
985115
985115
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
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
Dec 19 at 3:07
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
Dec 19 at 3:05
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
Dec 19 at 3:07
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
– Jay Patel
Dec 19 at 3:05
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
Dec 19 at 3:07
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
Dec 19 at 3:07
add a comment |
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 Dec 19 at 3:07
Chris Custer
10.5k3724
add a comment |
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 Dec 19 at 3:07
Chris Custer
10.5k3724
add a comment |
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 Dec 19 at 3:07
Chris Custer
10.5k3724
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 Dec 19 at 3:07
Chris Custer
10.5k3724
answered Dec 19 at 3:07
Chris Custer
10.5k3724
answered Dec 19 at 3:07
Chris Custer
10.5k3724
answered Dec 19 at 3:07
Chris Custer
10.5k3724
10.5k3724
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045924%2fwhy-is-it-called-commutative-property%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
Dec 19 at 2:48
2
I think of it like a commuter train. They move around or switch places. Well, not when I was in elementary school when I was expected to know those terms, as I didn't even know the word commuter, but later in high school I did, when no one cared about those properties anymore, lol.
– Octopus
Dec 19 at 5:24
1
As often, the best source for this kind of questions is Earliest Known Uses of Some of the Words of Mathematics : see COMMUTATIVE and DISTRIBUTIVE.
– Mauro ALLEGRANZA
Dec 19 at 16:01
@Octopus lol I never cared until it kept reoccuring when studying math in university (algebra, fields, subspaces etc.)
– Jay Patel
Dec 19 at 18:28