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由 cloudsea 於 星期五 二月 24, 2006 12:35 am
謝謝......^^
由 linch6123 於 星期四 二月 23, 2006 10:05 am
#ed_op#DIV#ed_cl#Let f(x)=sin(1/x) for x in (0,1)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#then#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# f(1/(2npi+pi/2))-f(1/(2npi))=1#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#but#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# ( 1/2npi+pi/2)-(1/2npi)→ 0 when n is large #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#therefore #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#f(x)=sin(1/x) for x in (0,1) is continuous and bounded ,but f(x) is not uniformly continuous #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
[問題]能幫我解解看這題應該算高微的問題嗎?
由 cloudsea 於 星期四 二月 23, 2006 7:13 am
#ed_op#DIV#ed_cl#Let -∞<a<b<∞ . Prove or disprove the following statement : If f :(a,b)→ R is continuous and bounded , then f is uniformly continuous on (a,b) #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#自己想的時候...覺得是true...因為是bound所以找不到例子...想證true時，想用定義證卻一直配不太出來...希望高手解惑....謝謝#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#