"The more laws, the less justice." -- Cicero

Thanks for the references.

I think you will agree that the bulk of your comment employs a post-set-theory nomenclature.

Regarding "if you were to choose a point completely at random, the odds of that point being another rational is zero", I ponder the question of how one might casually "choose" a value with infinite entropy.

Ah, but it's worse than this. The truly ambitious ladder climber creates not just unnecessarily complicated abstractions, but organizations. Processes for people to follow. Infrastructure for people to maintain. Committees to vet changes. Standing meetings.

Let me guess: the point of the interview was to see if he was a "team player".

I think you are getting away from my point, which pertains to what the article said, which is that mathematicians thought there were "gaps". What mathematician? Can I see the original quote?

The linguistic sleight-of-hand is what I challenge. What is this "gap" in which there are no numbers?

- A reader would naturally assume the word refers to a range. But if that is the meaning, then mathematicians never believed there were gaps between numbers.

- Or could "gap" refer to a single number, like sqrt(2)? If so, it obviously is not a gap without a number.

- Or does it refer to gaps between rational numbers? In other words, not all numbers are rational? Mathematicians did in fact believe this, from antiquity even ... but that remains true!

Regarding this naive construction you are referring to: did it precede set theory? What definition of "gap" would explain the article's treatment of it?