bhk
Joined 11 years ago
Joined 11 years ago
In my experience, the worst part of the C standard library is not its existence, but the fact that so many developers insist on slavishly using it directly, instead of safer wrappers.
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.
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?