Not just the string-related functions. If you want robust error checking, re-entrant code, and bounds checking performed in library functions (instead of performing bespoke validations all across your code base), you have some work to do. Yes, some improvements have been tacked on over the years, but many problems ("current locale", for one) remain endemic.
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.
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.
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?
Extraordinary claims require extraordinary evidence. Can you cite any claims by mathematicians that there were "gaps"? It isn't even true for rational numbers that you can identify an unoccupied "gap".
And by the way, what the Hell is up with all these people claiming that two spaces is an obsolete typewriter-era pre-proportional-font thing? Narrow proportional spaces make two spaces after a period MORE important for visually separating sentences. Is it old fashioned to think logically?
Funny enough, vanity sizing strikes there too. The purported waist size of a pair of Levi's is off by almost three inches.
One might argue that the size on their label is not supposed to indicate the size of the garment waistband, but the waist size of the wearer who would find it comfortable, but even with that interpretation it doesn't work out right.
Hold on there. High fiber consumption increases the excretion of cholesterol, by reducing the reabsorption of the cholesterol in bile. The liver produces cholesterol for bile, which mixes with our food in the duodenum and aids absorption of fats. Most of this cholesterol is then re-absorbed by the small intestines. By increasing bulk, fiber reduces the amount that is re-absorbed.
Effects on but biome are real too, and apparently beneficial, and may factor in, but it isn't the only (or necessarily the primary) mechanism for reducing serum cholesterol.
1g/lb is in fact a popular target among bodybuilders.
Much research indicates 0.5 to 0.7 g/lb provides most of the benefits, with continuing but diminishing gains above 0.7 g/lb. And the benefit is not just for "body building", but also for minimizing muscle loss during weight loss and improving insulin sensitivity. Other research indicates we may benefit from higher levels as we age.
Re: "99% of the time" ... this is an ambiguous sample space. Soundness of results clearly depends on the questions being asked. For what set of questions does the 99% guarantee hold?
Consider this analogy: Instead of using a root command shell, it is wise to use an account with appropriately restricted capabilities, to limit the downsides of mistakes. Cloud services support the notion of access control, but not the notion of network resource usage limits. It's an architectural flaw.
Or do you always log in as root, like a real man, relying purely on your experience and competence to avoid fat-finger mistakes?
Oscullation/"anticipation" in transitions is so gimmicky and cartoonish. Living things don't move like that, and mechanical things don't unless they are broken, chintzy, or poorly designed (underdamped).
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.