4 ms·
It's rather purple prose, but it's entirely meaningful. Maybe it doesn't seem to mean anything until after you know some linear algebra, though...
by wrs 2y ago
It's rather purple prose, but it's entirely meaningful. Maybe it doesn't seem to mean anything until after you know some linear algebra, though...
- dxbydt 2y agoits been a long time, but when i was taught this material, i was told there are only 3 cases - x+y=1, x+y=2 clearly has no solution since two numbers can’t simultaneously add to both one and two. x+y=1,2x+2y=2 clearly has infinitely many solutions. There’s only one equation here after canceling the 2, so you can plug in x’s and y’s all day long, no end to it. x+y=1, 2x+y=1 clearly has exactly one solution (0,1) after elimination. This example stuck with me so I use it even now. The author/Claude/Gemini/whatever could have just used this simple example instead of “trichotomy of curves through space conjoin through the realm of …” math, not Shakespeare.
- wrs 2y agoSure, but saying something in an ornate way is not the same as “saying nothing”.
- BlueTemplar 2y agoAlso, isn't this a great example of "when you have a hammer, everything looks like a nail" ? To explain this I would first and foremost use a picture, where the 3 cases : parallel, identical, intersection can be intuitively seen (using our visual system, rather than our language system), with merely a glance.