→ kerwinhui : 題目沒出錯，c=m/n則0=/=|p_k-cq_k|>=1/m -/-> 0 09/20 15:11
推 LPH66 : 一個符合條件的例子: p_n/q_n是無理數c的漸近分數 09/20 16:30
→ LPH66 : r_n 則是漸近分數跟這無理數之間的差距估計上界 09/20 16:31
→ agga : 果然是用到離散性 09/20 18:32
Let c be a real number.
Suppose that there exist seqiences of integers
{p_n} and {q_n} and a sequence of real number {r_n}
such that
(a) lim r_n=0
n->00
(b) 0< |p_n-c*q_n|<r_n, n>=1
show that c must be a irrational number
想問的是題目有沒有出錯, c應該要市 rational number.
又如果是rational number, 要如何證呢?
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