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## Main Question or Discussion Point

I have tried to search on the internet for a clear and concise definition for the mathematical term "pointwise," but I cannot find one that is comprehensible. The context of needing an answer to this question is this: "operations on real functions in a vector space are defined pointwise, such that ##f_1 + f_2 = f_1(x) + f_2(x)##, and ##af = a(f(x))##, where a is a scaler." In this context, what does pointwise mean?