作者adcores5 (adcores5)
看板Math
標題[代數] 一題代數
時間Mon May 9 10:42:33 2011
let K be a subfield of C which is not contained in R.
Prove that K is a dense subset of C
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1F：→ empty24 :C/R是finite extension,所以K/R也是 05/09 10:55
2F：→ empty24 :推得K要不然是R要不然跟C同構,因此K就是C 05/09 10:56
3F：→ empty24 :抱歉 看錯了 05/09 10:58
4F：推 LimSinE :設K'= Closure of K 是體，Q<K故R<K', R=/=K'→K'=C 05/09 11:50
5F：推 CFE220 :each subfield of C contains every rational number 05/09 21:16
6F：→ CFE220 :朝這方向思考會如何勒? 05/09 21:17