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Ah good I was looking for the restriction b ≠ 0 but couldn't find in on the Wikipedia page. Forgot to check out PlanetMath, thanks.


I'm actually surprised by the lack of rigor in many of the sources I checked. It's obvious that b != 0 is necessary because otherwise you can't get results like line segments having an infinite number of points, and hence equal to the amount of points in a line.[1] The thing is, a lot of common references seem to leave out that the endpoints can't be equal.[2] It's so obvious that it's just implied, but it's dangerous to treat mathematics like that!

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[1] http://mathworld.wolfram.com/LineSegment.html

[2] Just saying 'two distinct endpoints' instead of 'two endpoints' would work, so it's literally just one word that makes a big difference!




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