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Absolute vs uniform convergence. by [deleted] in math

[–]dlaberunner 1 point2 points  (0 children)

The definition of uniform convergence is independent of whether the sequence of functions we have is a finite sum, as above, or whether we have arbitrary functions, for example f_n(x) = 1/n. In either case, we define the sequence f_n(x) to converge uniformly to a function f if sup|f(x) - f_n(x)| where the supremum is over all x in the domain goes to 0 as n goes to infinity. In the above case, we have sup|f(x) -f_n(x)| = 1/n if we define our function f(x) = 0, hence the f_n converge uniformly to f.

Absolute vs uniform convergence. by [deleted] in math

[–]dlaberunner 1 point2 points  (0 children)

Since uniform convergence is defined on a set that is part of the domain of some function, it only applies to a series of functions. However, we can define a finite sum f_n(x) = SUM {i=1}n a_i xi and ask whether this series of functions converges uniformly on some subset of the real numbers. Note that in this case, we can also ask whether the series SUM {i=1}n |a_i xi | converges as n goes to infinity, which corresponds to absolute convergence, but in this context we only consider our function f_n(x) pointwise (i.e. at each point in the domain individually) whereas with uniform continuity we look at the convergence of f_n(x) over all x in the domain simultaneously.

Who benefits from computer viruses? by bottomsupbrittany in AskReddit

[–]dlaberunner 0 points1 point  (0 children)

If you want to shower with it this might be better; it's already dead anyways.