[分析] 高微(8)

看板Math作者 (批踢踢基金只進不出)時間20年前 (2005/07/23 03:42), 編輯推噓1(1推 0噓 4→)
留言5則, 1人參與, 最新討論串1/1
Let S ={ m + na | a in R-Q, m,n in Z }. Show that S is dense in R. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.218.142
推
218.175.92.177 07/23, , 1F
先考慮na dense in (0,1)
218.175.92.177 07/23, 1F
→
218.175.92.177 07/23, , 2F
exist n>0 minimum such that na>1 (n-1)a<1
218.175.92.177 07/23, 2F
→
218.175.92.177 07/23, , 3F
set na-1=a_1 consider ma_1 again
218.175.92.177 07/23, 3F
→
218.175.92.177 07/23, , 4F
一開始改成na mod 1 dense in (0,1)
218.175.92.177 07/23, 4F
→
218.175.92.177 07/23, , 5F
continue this manner Q.E.D
218.175.92.177 07/23, 5F
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文章代碼(AID): #12uKn3kl (Math)