Howtosignalprocessing
What is a limit in a sequence?
The limit of a sequence is the value the sequence approaches as the number of terms goes to infinity. Not every sequence has this behavior: those that do are called convergent, while those that don't are called divergent. Limits capture the long-term behavior of a sequence and are thus very useful in bounding them.
What is the limit of a sequence of functions?
The sequence (fn) of functions converges pointwise on A to a function f :A→R, if for every x∈A, fn(x)→f(x) as a sequence of real numbers. The function f in the above definition is called the limit function, and the convergence is denoted by fn →f, limfn =f, or limn→∞fn(x)=f(x).
