3 ms·
I think you are mistaking the fact that you can easily find an example satisfying the theorem’s statement with the proof that the statement is always true. Of c
by chenb4425 2mo ago
I think you are mistaking the fact that you can easily find an example satisfying the theorem’s statement with the proof that the statement is always true. Of course given any set of points that aren’t all on the same line, your nine your old could find a line passing through only two points. But could they explain to you why this is always possible, no matter the configuration of points? You can’t just say “I draw a line between two points and that’s it.” You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me).
- stackghost 2mo ago>You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me). There isn't a third point on the line you found because the problem stipulates that the set of points is not collinear.
- chenb4425 2mo agoThat's only assuming your set of points only contains three points. If you have four or more points, it's entirely possible that a line you draw between two points passes through a third. . ... If you're given the above set of points, it's obviously not collinear due to the point at the top, but if you draw a line through any of the bottom two points, it will hit a third.
- h3lp 2mo agoSo it says that not ALL points are on that single line. But it doesn't stipulate that THREE points can't be on the line---the theorem is about proving that you can find one that doesn't have the third point.