看到一道题，大家看我证明有没有问题。题如下： Let f: R->R be a continuous function, given f(q)=0 forall q in Q (rational number set). Prove that f(x)=0 forall x in R (real number set).
我的证法： forall epsilon>0, let U be the open set B(0, epsilon) in R (R is the Euclidean topology), then Q in f^{-1}(U). Since f is continuous and R is the smallest open set comprising Q, so f^{-1}(U)=R. Also since epsilon is arbitrarily small, so f(R)=0.
【 在 freelikewind (像风一样自由) 的大作中提到: 】 : 最近把小时候的书在网上搜到不少电子版，方便多了。 : 没事儿也顺便做做题，当娱乐了。 : 看到一道题，大家看我证明有没有问题。题如下： : Let f: R->R be a continuous function, given f(q)=0 forall q in Q (rational : number set). : Prove that f(x)=0 forall x in R (real number set). : 我的证法： : forall epsilon>0, let U be the open set B(0, epsilon) in R (R is the : Euclidean topology), then Q in f^{-1}(U). : Since f is continuous and R is the smallest open set comprising Q, so f^{-1} : ...................
最近把小时候的书在网上搜到不少电子版，方便多了。
没事儿也顺便做做题，当娱乐了。
看到一道题，大家看我证明有没有问题。题如下：
Let f: R->R be a continuous function, given f(q)=0 forall q in Q (rational
number set).
Prove that f(x)=0 forall x in R (real number set).
我的证法：
forall epsilon>0, let U be the open set B(0, epsilon) in R (R is the
Euclidean topology), then Q in f^{-1}(U).
Since f is continuous and R is the smallest open set comprising Q, so f^{-1}(U)=R.
Also since epsilon is arbitrarily small, so f(R)=0.
没问题。
【 在 freelikewind (像风一样自由) 的大作中提到: 】
: 最近把小时候的书在网上搜到不少电子版，方便多了。
: 没事儿也顺便做做题，当娱乐了。
: 看到一道题，大家看我证明有没有问题。题如下：
: Let f: R->R be a continuous function, given f(q)=0 forall q in Q (rational
: number set).
: Prove that f(x)=0 forall x in R (real number set).
: 我的证法：
: forall epsilon>0, let U be the open set B(0, epsilon) in R (R is the
: Euclidean topology), then Q in f^{-1}(U).
: Since f is continuous and R is the smallest open set comprising Q, so f^{-1}
: ...................
李永乐把成年人叫小朋友
楼主把大学叫小时候
现在想起来当年在国内念书时那种风花雪月的生活，
恍若隔世。
【 在 bobolan88 (波波熊) 的大作中提到: 】
: 李永乐把成年人叫小朋友
: 楼主把大学叫小时候