[數撚圍爐區] Let ε < 0. (9)

first learn or referebce

有冇大神話我知點解if lim sup an= lim inf an, then lim an exist，但唔準用subsequence prove

簡單黎講咪 S = limsup, I = liminf
但係得finite 咁多個term係 [I - e, S + e] 出面
但 I = S, 自己用epsilon N 補完

Right hand limit 係咪可以當limsup

係咁出applied 紙係咪會chok高排名

Probability theory 同 Sheldon Ross 本 first course in prob.講嘅嘢係咪完全唔同

冇curriculum睇點答你有啲地方只係maths啲嘅ross，有啲地方會用measure

話說mul cal有無俾懶人嘅counterexample list諗住midterm之前背下counterexample

見有啲prob.嘅proof用measure好似三行搞掂 用正常方法就要搞一輪

mul cal要咩counter example?
all partial derivative exists but not differentiable?

呢類啦

仲有例如唔係C^k導致唔可以exchange啲variable
all directional derivatives exist but not differentiable
所有y = mx嘅path都有同一個limit但係個limit唔exist
呢類嘢

take path 果D可以試下chok下d level set, 2 variables如果有兩條curve相交咪搞掂
又或者chok d rational functions of homogeneous polynomial再用y = x^k搞搞

交換d ge次序果個我諗唔到有咩方法造出黎
我估可以由D differentiable but the derivative is not continuous ge function chok起 (同埋好似有個classical example?)