Though now that I think about it, if the difference is some irrational number then this seems to work, as any set Xi would contain exactly one unique rational number. Now they each have the cardinality of R, and the family has the cardinality of Q. And then it all seems to work. Does that seem right?
Though now that I think about it, if the difference is some irrational number then this seems to work, as any set Xi would contain exactly one unique rational number. Now they each have the cardinality of R, and the family has the cardinality of Q. And then it all seems to work.
Does that seem right?
That sounds like it also works. I’ve seen the proof both ways and I think I was mixing them together in my head.