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Try to come up with a set non-colinear points where NO line passes through two and ONLY TWO points and you'll see the value of the statement. You may think "I'
by glimshe 2mo ago
Try to come up with a set non-colinear points where NO line passes through two and ONLY TWO points and you'll see the value of the statement.
You may think "I'm sure I can arrange these points in a way where EVERY line will cross three or more points" but you will fail if you try unless ALL points are colinear.
- scythe 2mo agoThis is true for finite sets. For infinite sets, the Sierpinski triangle is a counterexample.
- ky3 2mo ago> the Sierpinski triangle is a counterexample How so? It's bounded by the large initial triangle. The line containing any two of the vertices doesn't intersect any other point.
- tzs 2mo agoThat’s an uncountable set. If we want a counter example for uncountable sets a simpler example is a circular area. Anyone happen to know if it is true for countably infinite sets?
- namibj 2mo agoJust a regular grid? That's countable you just go in a spiral.
- JetSetWilly 2mo agoYou can always find a line that passes between two points. Why would you even try to find a line that doesn’t pass between two points? What is the difficult part here.
- ky3 2mo agoFind one that bridges only two points, no more. Unless ofc you're given a configuration that's obviously impossible: all of them in a line.
- glimshe 2mo agoThe difficult part is that you may think that there's an arrangement where you could force every line to go through 3 or more points. The line extends to infinity, keep in mind.