Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confusing subtraction

  1. May 19, 2005 #1
    Well, you might consider my remark to be really silly :smile:. I was thinking about subtraction of reals and the following ideas came to my mind:

    From one side, we may consider subtraction to be addition of the inverse of an element, for example:

    (5 - 3) - 2 = (5 + (-3)) + (-2).

    This "version" of subtraction is associative and (5 + (-3)) + (-2) = 5 + ((-3) + (-2)).

    On the other side, if we treat subtraction separately from the addition, it is not associative:

    (5 - 3) - 2 is different from 5 - (3 - 2).

    Kocur.
     
  2. jcsd
  3. May 19, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Yes,it's actually the "+" operation (called addition) that comes into abstract fields,rings and algebras definition.

    As u can check,"+" is an associative operation.

    Daniel.
     
  4. May 19, 2005 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    In general mathematicians do not consider "subtraction" to be a distinct operation- largely because it would not be associative and associative is a very nice property.
    Subtraction is simply shorthand for "add the additive inverse" and, of course, addition is associative.
     
  5. May 19, 2005 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Hopefully, Kocur, you've understood from the previous replies that your remark wasn't silly at all.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Confusing subtraction
  1. Simultaneous confusion (Replies: 9)

  2. Quaternion confusion (Replies: 3)

Loading...