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?






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  • I've always wondered this, but apparently never enough to ask! +1
    – Matt Samuel
    33 mins ago















up vote
1
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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







share|cite|improve this question
























  • I've always wondered this, but apparently never enough to ask! +1
    – Matt Samuel
    33 mins ago













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







share|cite|improve this question















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






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edited 19 mins ago









Eevee Trainer

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asked 39 mins ago









Jay Patel

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  • I've always wondered this, but apparently never enough to ask! +1
    – Matt Samuel
    33 mins ago


















  • I've always wondered this, but apparently never enough to ask! +1
    – Matt Samuel
    33 mins ago
















I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
33 mins ago




I've always wondered this, but apparently never enough to ask! +1
– Matt Samuel
33 mins ago










3 Answers
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4
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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.







share|cite|improve this answer

















  • 1




    Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
    – Christopher Marley
    31 mins ago


















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!






share|cite|improve this answer





















  • I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
    – Jay Patel
    16 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
    14 mins ago


















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.






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    3 Answers
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    3 Answers
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    up vote
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    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.







    share|cite|improve this answer

















    • 1




      Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
      – Christopher Marley
      31 mins ago















    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.







    share|cite|improve this answer

















    • 1




      Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
      – Christopher Marley
      31 mins ago













    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.







    share|cite|improve this answer












    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.








    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 37 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
      31 mins ago














    • 1




      Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
      – Christopher Marley
      31 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
    31 mins ago




    Nice etymology! I'll just add "commutare" from Latin, meaning, "to exchange," from which the French "commuter" is derived.
    – Christopher Marley
    31 mins ago










    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!






    share|cite|improve this answer





















    • I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
      – Jay Patel
      16 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
      14 mins ago















    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!






    share|cite|improve this answer





















    • I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
      – Jay Patel
      16 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
      14 mins ago













    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!






    share|cite|improve this answer












    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!







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 34 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
      16 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
      14 mins ago


















    • I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
      – Jay Patel
      16 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
      14 mins ago
















    I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
    – Jay Patel
    16 mins ago




    I like this a lot since I speak english. (Commutative, communication meaning exchange). The other explanation uses french / latin words.
    – Jay Patel
    16 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
    14 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
    14 mins ago










    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.






    share|cite|improve this answer

























      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.






      share|cite|improve this answer























        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 14 mins ago









        Chris Custer

        10.3k3724




        10.3k3724






























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