Hi all, I have a question Concerning Beck's theorem. I have read it from http://en.wikipedia.org/wiki/Beck%27s_theorem and I have two questions :

I suppose Beck's theorem doesn't hold when instead of saying "at least two points" we take "exactly two points",since there may be lines which do not connect exactly two points at all, right?

In the proof mentioned above, I think the statement that

is incorrect, it should be "fewer than C points" or more than "2n/C points". Am I right or do I miss some logic here?*"The lines that connect these pairs either pass through fewer than 2C points, or pass through more than n/C points."*

thanks