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Math Help - Subtraction in F3 Field 1-2-1

  1. #1
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    Subtraction in F3 Field 1-2-1

    Hi,

    consider the field \mathbb{F}_{3}

    The composition table should look like:

    0+0=0
    0+1=1+0=1
    0+2=2+0=2
    1+1=2
    1+2=2+1=0
    2+2=1

    0*0=0=0*1=0*2=1*0=2*0
    1*1=1
    1*2=2*1=2
    2*2=1

    No I have the case that I have to calculate:

    1-2-1=?

    I guess it would be zero but I am not sure

    How to do this?

    Thank you for helping
    greetings
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  2. #2
    Moo
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    Hello,

    1-2-1=(1-1)-2=-2=1

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  3. #3
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    Hi,

    first: Thanks for help

    second: Could you explain me why this is one? I don't got it

    greetings
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  4. #4
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    Quote Originally Posted by Herbststurm View Post
    Hi,

    first: Thanks for help

    second: Could you explain me why this is one? I don't got it

    greetings
    The fundamental problem with the subtraction operator is that it is NOT ASSOCIATIVE! For example, 1 - (2 - 1) \neq (1 - 2) - 1
    Thus parantheses cant be dropped.

    So I will interpret 1 - 2 -1 as 1 + (-2) + (-1) = 1 + 1 + 2 = 1
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  5. #5
    Moo
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    Quote Originally Posted by Isomorphism View Post
    The fundamental problem with the subtraction operator is that it is NOT ASSOCIATIVE! For example, 1 - (2 - 1) \neq (1 - 2) - 1
    Thus parantheses cant be dropped.

    So I will interpret 1 - 2 -1 as 1 + (-2) + (-1) = 1 + 1 + 2 = 1
    Where did anyone mention associativity ?
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  6. #6
    Lord of certain Rings
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    Quote Originally Posted by Moo View Post
    Where did anyone mention associativity ?
    Well the problem is how you interpret 1-2-1. Are you thinking of "-" as an operator OR are you thinking of "-x" as a representation for additive inverse?

    How do you justify the sequence of operations in your asnwers 1-2-1=(1-1)-2=-2=1?
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  7. #7
    Moo
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    Quote Originally Posted by Isomorphism View Post
    Well the problem is how you interpret 1-2-1. Are you thinking of "-" as an operator OR are you thinking of "-x" as a representation for additive inverse?

    How do you justify the sequence of operations in your asnwers 1-2-1=(1-1)-2=-2=1?
    Adding the inverse.
    Yes, you normally would have to write 1+(-2)+(-1), but this is now how it was stated.
    And for simplification, you directly write 1-2-1.

    What I did was not using any commutativity of the subtraction. 1-2-1 becoming 1-1-2 is the commutativity of the addition. It's just that it's simplified and not written 1+(-1)+(-2)
    After that, it's still associativity, for addition. For the same reasons.
    Last edited by mr fantastic; January 23rd 2009 at 01:26 PM.
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