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by rsy96
3939 days ago
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> Well, I find whole thing rather controversial, so to say. Depends on what do one mean by "collection" and by "point", eg. if we take point literally: (x, y) \in RxR, then we have to assume that "collection" is uncountable (which seems counterintuitive, esp. from the school student's pov). OTOH, one could treat "point" as representation of that point, eg. pencil mark, so that point is no longer single element, but rather an uncountable subset containing the point of interest, along with its neighbourhood => our "collection" becomes countable, so we could think about it as bunch of indexed points (much more intuitive, isn't it?), shifting our attention towards mapping's representation from the mapping itself. The whole paragraph does not make sense to me. For example, how is a collection uncountable somehow unintuitive? Why should a point not be a single element, but a subset or a pencil mark? Are you confusing the theoretical graph with the graph actually drawn (which has finite width)? |
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- 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 :)