※ 引述《jenny0911820 (air)》之銘言：
: ※ 引述《jenny0911820 (air)》之銘言：
: : Srppose that Xn屬於R
: : Prove that {Xn}is bounded iff there is a C>0 such that |Xn|<=C
: : for all n屬於N(自然數)
: : 煩請各位高手幫幫我
: : 謝謝!!
: : 小女子感激不盡!!
: Def:(1){Xn}is said to be bounded above iff there is
: M屬於R such that Xn<=M for all n屬於N
: (2){Xn}is said to be bounded above iff there is
: m屬於R such that Xn>=m for all n屬於N
: (3){Xn}is said to be bounded iff it is bounded both
: above and below.
: Srppose that Xn屬於R
: : Prove that {Xn}is bounded iff there is a C>0 such that |Xn|<=C
: : for all n屬於N(自然數)
: 以上是補充定義的部份!!
: 謝謝大家!!
=>
{X_n} 有界 <=> {X_n} bounded above and bounded below.
所以存在 M , m 使得
m < X_n < M 對於所有的 n 均成立
取 C = max (|m|,|M|)
則 C > 0 且 |X_n| < C
<=
由假設 -C < X_n < C, 對於所有的 n 均成立
所以由定義 {X_n} bounded above and below
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