Copy of Uniform convergence 2

התכנסות במ"ש uniform
[math]\forall\epsilon>0,\exists N:\forall x\in D,n>N\Rightarrow\forall n>N:|fnx-fx|<\epsilon[/math]
This applet demonstrates that f_n(x) = 2nx/(1 + n^2 x^2) converges to f(x) =0 uniformly on (a, infinity) for any a>1, but not uniformly on (0, infinity).
התכנסות נקודתית pointwise
[math]\forall\epsilon>0,x\in D\exists N\Rightarrow\forall n>N:|fnx-fx|<\epsilon[/math]
This applet demonstrates the pointwise convergence of f_n(x) = e^(n(x-1)) to f(x) =0 on (0,1).
– Yasmin Nizan, peressamuel

Information: Copy of Uniform convergence 2