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I am trying to prove that axioms A1, A2, A3, A4, M2, D hold.

so A1 :

$$ a+b=b+a$$ $$x+x+x+x=x+x+x+x$$ $$4x=4x$$ Am I on the right way?

  • 3
    I don't think you are. I understand that your Axiom 1 says that if you take two elements $a$ and $b$ then $a+b=b+a.$ You have only one element in this set, that is $x$. So you have to take $a=x$ and $b=x$. We have $a+b=x+x=x=x+x=b+a.$2012-03-09
  • 4
    What does $x+x+x+x=x+x+x+x$ have to do with anything?2012-03-09
  • 0
    @Chris: Best guess: the OP is reckoning that the only element is $x+x$ and substituting that for both $a$ and $b$ in the statement of commutativity.2012-03-09
  • 1
    Name your element $x$ by $0$ and everything will make more sense.2012-03-09
  • 4
    You need to tell us what you mean by A1, etc. These are labels in your texbook, not universally accepted labels.2012-03-09

3 Answers 3