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| ``Re: Imaginary irrational number?''
by alozano on 2007-04-15 18:33:15 |
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| mathcam asks: I agree with the first (unquoted) part of your post, but I think this last definition is unsatisfactory -- What are the rational numbers in an arbitrary field of characteristic zero (i.e. what are the integers)?
Let K be a field of characteristic zero. Then there is a "one" element in K, call it 1, and n times 1 = 1+...+1 (n times) is not zero for any natural n (because of the assumption on the characteristic). The numbers n x 1 are your integers. Also, since K is a field, every n x 1 (not zero) has an inverse which we call 1/n. Thus, there is a copy of Q (or isomorphic to Q) inside K.
Alvaro |
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