Re: [分析] uniformly continuous
Since lim f(x) = L
we have for all ε>0, there exists M > 0 s.t.
for all x ≧ M, |f(x) - L| < ε
1.for xε[0,M], f(x) is uniformly continuous.
(continuous mapping with a compact domain is an uniformly continuous mapping)
2.for xε[M,oo), we write down the definition：
for x,y ε[M,oo), for all ε>0 , any δ>0 (比there exists 更強)
when │x-y│< δ
│f(x)-f(y)│=│f(x)-L+L-f(y)│≦│f(x)-L│+│f(y)-L│
< ε + ε = 2ε
(在[M,oo)這個區域,不管x,y取多少,一定會符合 |f(x) - L| < ε)
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不知道這樣可不可以@@"
好久沒碰高微了XD
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