My spoiler has only the task, I didn't want to show it verbatim because of the authors copyright.
If you follow the links you'll see that your solution is optimal.
But I would hide your number behind spoiler tags too. :)
I'll wait some days before showing my proof.
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> Update: I had expected more information from following the link
Behind the link is another link to the "solution", with another comment section. With various so called proofs, which I didn't find understandable or convincing.
Ignore the comments about "less vs fewer"
Except the one saying there should be a special hell for people nagging about grammar in a math blog.
> Waiting for lanx's proof
Please remind me next weekend. :)
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[d/l] |
That's the way I used to think of it, despite the fact that it doesn't hold up in a plethora of real life, real English situations. And since you specifically invoked "For those involved with computers", my first exception will be an example familiar to any Monk here:
In Perl, $a < $b would be said "scalar a is less than scalar b", despite the fact that, whether the scalar is an IV or NV or Math::BigRat, scalars a and b are always digital.
In mathematics, a < b is said "a is less than b", whether "a,b ∈ ℝ" (a and b are elements of the set of real numbers: analog) or "a,b ∈ ℤ" (a and b are elements of the set of integers: digital)
In science, light comes in discrete (digital) packets called photons, but "there is less light in the dark cave then outside in the bright sunshine".
"The count of the fingers I am holding up on my right hand (2) is less than the count of the fingers I am holding up on my left hand (4)", despite the fact that my fingers are quite obviously digital. (Sorry, I had to make that pun.) (I was going to originally use "quantity" rather than "count" in that example, but "quantity" isn't as restricted to digital as "count" is, so I switched to "count" to emphasize the digital nature of the values involved.)
As far as I can think of, "fewer" is only used for digital items (though I'd love to learn exceptions in that direction, too, to annoy the pedants), but "less" isn't as restricted to analog as some people claim.
There are many places where I think "less" sounds better to my ears than "fewer", but phrases like "10 items or less" doesn't bother me anymore, because there are too many exceptions for the rule ''"less" is always analog'' to carry the weight that I used to think it did.
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[d/l]
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"less" is analog,
"fewer" is digital.
The problem is that many people — I mean sophomoric pedants — believe many quantities are discrete when in fact they are continuous.
Take age, for example. A pedant might insist that "Bobby is less than ten years old" is incorrect, and must be phrased as "Bobby is fewer than ten years old".
But a person's age is not really an integer number of years, it is a float amount of time. :-) "Ten years old" is a watermark; if one has not yet reached that watermark in age, then they are less than that.
You see people making this ridiculous "correction" all the time.
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Hey
> > Waiting for lanx's proof
> Please remind me next weekend. :)
I got messages asking me when I'm posting the proof.
I wanted everybody interested to have a chance to see the task and attempt to
find a(nother) proof.
Please /msg [lanx] if you want me to wait till the weekend.
Otherwise I'll post it tomorrow.
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