- #1
lom
- 29
- 0
[tex]f_n(x)=1,1\leq x\leq n\\[/tex]
[tex]f_n(x)=0,1< n< \infty[/tex]
f_n converges to f which is 1
at the beggining f_n is 0 but when n goes to infinity its 1
so why sup(f_n(x)-f(x))=1 ?
f is allways 1
but f_n is 0 and going to one
in one case its 1-1
in the other its 0-1
the supremum is 0
so the supremumum of their difference is 0 not 1
?
[tex]f_n(x)=0,1< n< \infty[/tex]
f_n converges to f which is 1
at the beggining f_n is 0 but when n goes to infinity its 1
so why sup(f_n(x)-f(x))=1 ?
f is allways 1
but f_n is 0 and going to one
in one case its 1-1
in the other its 0-1
the supremum is 0
so the supremumum of their difference is 0 not 1
?