Philosophy - #10 and 9

Both brain-twisters #10 and #9 suffer from an inconsistent definition. Let's take them one at a time, starting with #9.

Take a set of numbers. The "interesting" number is the smallest (in this puzzle). But then, after removing that one, there is still a smallest number. Keep removing the interesting (smallest) number, the argument goes, and you will be left with no "uninteresting" numbers.
But, when you remove the smallest number, you've created a new set! Start again with the initial set; there is a smallest number, but the rest are still uninteresting IN THAT SET. If there are "n" numbers, "n-1" of them are uninteresting. Just stop there. If you remove that number from the set, you've changed the system.

#10 has the same problem. (And actually, I really liked that this problem was included. I used to think along these lines in elementary school when I was home sick for the day. My mom insisted that I go to school unless I had a fever. I used to wonder when the exact minute was that I was officially "sick." And then I'd wonder if I could break it down further - into the exact second, or millisecond, or microsecond that I transitioned from being "well enough to go to school" to "sick enough to stay home." Apparently I was a 6-yr-old philosopher. But I digress.)

Few things in life are in a simple binary state. If someone showed me a millions grains of sand, I'd probably say, "That's a heap of sand!" If someone showed me a single grain of sand, I'd certainly NOT say, "That's a heap of sand!" But this isn't a simple on / off switch. Just as, when I was a child, illness would come on gradually, with an intermediate "take a nap, then see if you're well enough to go to school late" phase, there is a gradient between "heap" and "single grain." Maybe a hundred thousand grains is a "pile." And ten thousand grains is a "lump." There might even be a single-grain difference between what I'd call a "pile" and what I'd call a "lump." But I wouldn't necessarily keep calling a collection of sand a "heap" until I got down to one grain. At some point along that gradient, I'd go into the next label.