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February 19th, 2011, 04:07 AM  #1 
Member Joined: Nov 2010 Posts: 34 Thanks: 0  Little question about the field axioms
Hi! I have seen that in proofs, they often omit several of the field axioms. In fact, they usually just show that the set and the operator is closed under addition, subtraction, multiplication and division and the rest of the axoims sort of magicaly follows. I think there is some result that allow one to do this (As I have mentioned in earlier post`s). I have gone over my book several times, but for some reason I still cannot find the reason. I would be very happy if someone could help me. 
February 19th, 2011, 04:59 AM  #2 
Senior Member Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0  Re: Little question about the field axioms
If you have a subset of field, then most of the field axioms are inherited. For example the real numbers form a field. So to check that the rational numbers form a field you need only check the various closures, and that 0 and 1 are in the set.

February 20th, 2011, 01:52 AM  #3 
Member Joined: Nov 2010 Posts: 34 Thanks: 0  Re: Little question about the field axioms
Ok, I see. Thank`s a lot. 

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