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Then you MUST study what Cantor did. You will find it beautifully logical. The set of Natural Numbers are countably infinite and any set...

IMO, this discussion should focus on the OP, which specified the counting size of sets. Otherwise, it can become very unfocused.

The problem statement specifies that all failures are independent. All links on that path are up. It indicates nothing about the ADB...

One take-away from this is how rapidly a simple problem can become unmanageable. Combinatorial problems grow exponentially and the...

I see. The solutions that depend on counting combinations of 3 lines don't work. That and the need for symmetry is key to most of the...

The first statement answered the question, --------------------------------------- Sure, but not every three non-parallel lines...

It certainly complicates symmetry arguments. Maybe I misunderstand your first statement. I don't see that it invalidates anything about...

2) The solution based on counting triads of intersecting lines. 1) E.g., if the figure doesn't include two triangles that I've erased...

On the subject of set sizes, it would benefit you to read about what Cantor did and how he approached the subject. IMHO, it has been...

I'm not sure what you mean here. 1) If an intersection is beyond the figure area, should it count as a possible triangle vertex or not...

I enjoyed thinking about it. Just for fun of finding an alternative approach.

IMHO, the desire for a non-"brute force counting" method is misguided here. The logic is so specialized and convoluted that it required...

I wrote a program to do brute force counting and its answer matches that of @bob012345 in post #15. I have not thoroughly examined the...

damn. this is hard to hear. @phinds was just a loved and core member for 15 years. Thank you so much for taking a bit of time to let us...

My deepest condolences. He will be missed.