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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).

  2. jcsd
  3. May 19, 2005 #2


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    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.

  4. May 19, 2005 #3


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    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


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    Hopefully, Kocur, you've understood from the previous replies that your remark wasn't silly at all.
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