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There are two points in that paragraph: - enumerable (countable) sets are more intuitive to reason about - no matter, how do you comprehend the function, you'll end up drawing it by means of composing continuous chunks > Are you confusing the theoretical graph with the graph actually drawn (which has finite width)?
Probably. From my point of view, graph is the something that is drawn/plotted, whilst relation/mapping being something that you've called "theoretical graph". So I'd question, how treating graph as a bunch of points is superior concept, giving that one could easily slip into substituting actual mapping's points by their graphical representation, for the sake of simplicity, thus possibly hiding mapping's behaviour from own mind. PS
Nevertheless, I do now understand, that the whole thing author has meant to say, was: "Given x = f(y), it is not only some explicit line on a plane, but also a mapping f: (x, y) \in RxR (which also could be drawn, btw)". The whole subthread is more of a dialectical excercise, with the definition of "graph" not being synchronized among participants :) |