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#1 2007-10-15 01:43:51
- xXxEmZyxXx
- Member
- Registered: 2007-10-15
- Posts: 12
Axioms for real numbers proofs!!!
hey if anyone could help me with the two following proofs by using the axioms for real numbers it would be very much appreicated!!!
1) Suppose c ER has the property that ca=a, for some non-zero aER. prove that c=1
2) Suppose x, y ,z are real numbers and Z<0 and X<Y. prove that XZ>YZ
thanks in advance 
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#2 2007-10-15 03:25:08
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: Axioms for real numbers proofs!!!
1. This has everything to do with additive inverses, the distributive property and the fact that two nonzero elements multiplied is nonzero.
2. This all depends on how much you are allowed to assume. The easiest (though most tedious) way to do it is by considering the four cases where X and Y are positive or negative.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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