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The authors of Raddit tried that, but found that actually running Reddit's software, especially on low-end hardware for a smaller community, was a pain in the arse and decided it'd be easier to build their own that fit their purposes.

Usenet, back in its heyday, might also qualify

If that's a genuine ethical issue then patents would be woefully inadequate at preventing it, since they would only provide a time-limited block. To actually fix things you'd need actual regulation, at which point the patent goes back to being bad.

"Denying service" in those cases is not conducting any further sales/etc with them.

It's not remotely disabling things they've previously bought from you.

That's quite a different kettle of fish.

I know -- I just apparently parsed Gaelic as Scottish and forgot that the spelling is same for Irish Gaelic...

We've had it for 2000 years, give or take...

I'm pretty sure the standard definition of primes permits only natural numbers.

Assuming "floating point" refers to things fitting the IEEE754 spec at some precision, I'm pretty sure there are still only countably many of them.

After all, for any specific size of mantissa and exponent, there will be a finite number of floats of that size, and there are a countable number of options for mantissa and exponent (corresponds to N²), thus the number of floating point values is countable.

Alternatively, each of them corresponds to an arbitrary length bitstring, in addition to a pair of numbers defining the mantissa and exponent, which would put them in bijection with N³ and thus also be countable.

EDIT: to add to that, I believe that one cannot in any meaningful way encode uncomputable values (in the sense that even if one introduces distinguished bitstrings intended to "encode" a specific¹ uncomputable value one can't do anything other than treat is as a distinguished value, and especially one can't perform arithmetic on it or print its digits or similar), so you'll still be limited to a countable set of floating point numbers even with other tricks.

¹ If that term even has meaning when dealing with uncomputable numbers...

It should be noted, the LG Prada predates the original iPhone by about 6 months, with largely the same design (to the degree that LG sued Apple alleging that the design was copied). Apple managed to capture the market, however, whereas LG didn't.

There's the old joke that the axiom of choice is obviously true, the well-ordering theorem is obviously false, and Zorn's lemma is too complicated to say.

This is a fair point.

I think the only axiom you need to rethink from ZF is powersets (since I think that's the only axiom that produces uncomputable sets from computable ones (ignoring the AC, briefly)). What you'd replace it with (some sort of one based on comprehension, presumably) I couldn't say though.

I tend to prefer considering the sets to encode bitstrings (encode a set as sum(2 ^ -x for x in X)), but yes the equivalence between computable sets and computable numbers is straightforward.

In this case, what you "throw out" are uncomputable (or non-recursive, depending on terminology you like) sets; i.e. sets for which the membership function is not decidable. Yes, there are an uncountable number of these sets, but they can't be defined in any useful way.