Given
pointwise on a domain
, where each
is monotone (either increasing or decreasing) on
, show that
is monotone on
.
so what I have is:
assume that f_n(x) is monotone increasing then:
therefore
No. The function f_n(x) is increasing in x, not n. The definition should be that if y>x then f(y)>f(x).
by definition (the one that I am using) a function is pointwise convergent if and only if
and if and only if given an
(dependent on both
and
)
such that
so based on that if I let:
(correct) and
No. This should be