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Comment by Smaug123 | Hacker News Reader

I'm not really a fan of that proof because it's a proof by contradiction in the least helpful sense. It doesn't tell you why the theorem is true; only that some assumption was wrong. Much better would be if the proof were accompanied by examples of systems that had CA but not P, CP but not A, and so on, to show that this result is best possible.

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So you are saying that to show that less is the best you can do would be the next step, and by extension you could ommit the first step and go directly to show cp or ap was optimal. But showing the contradictiin us what motivates the first step. Going the other way around, "thus cap is not in the set of optimals" shows less and begets the question.

"begets the question" is a beautiful solution to the "begs the question" error, but I think in this case you meant "begs the question"?

There's really very little reason to ever use that expression. It's not a particularly good translation of petitio principii, which is itself not a good translation of a previous text. The Latin is a less ambiguous way to refer to the logical concept, and "begets" or "provokes" similarly avoids confusion with the common sense. That said, I do think you might be right about which they wanted.

As far as I can tell begets is the original form, begs is a mondegreen. I am using this deliberately only since I came across [1], to say "escapes the question". Alas that's just an unsubstantiated hunch. Maybe I should just write "escapes".

[1] https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-Eur...

... which is akin to Latin fugio, fugere -- to flee. The analysis of OE begietan as be+get strikes me as faux-etymology fashioned after behold and the like, where beholden has little to do with holding, all the same.

This is a hobby of mine to the point of becoming neurotic. It's all in vein if a play of words needs explaining. It's still kind of insightful, if you'll entertain me a little longer.

If bʰegʷ- means to run, flee, then how is bʰeg-, to break, related? Why is to break rather reconstructed as bʰreg-. Why is bʰegʷ- given an alternative form bʰewg-? Does preḱ-, to ask, fit in here; or prey- or what it was with a related meaning? Maybe wreg-, whence wreck?

What about bag, pray, pay, fag, vag, way, weigh, etc etc.

Maybe to break away from always meant ''departure'', ''to go, run away''. Why are hurried news breaking? Why does German have "brandaktuell" instead, burning news? I have to break it to you, I don't know. I can already hear you begging the question to stop. But I have one more. Is a beggar someone living out of bags? I really don't want to know.

>It doesn't tell you why the theorem is true; only that some assumption was wrong.

A proof establishes truth, it does not typically explain. And yes, some assumption was wrong. The assumed premise was wrong. A system which is consistent, available, and partition-resistant does not exist. The truth of the theorem that no such system can exist is proven. I imagine it's not the proof you dislike, but the article about it which you wish had more explanation which is reasonable. It would be a different matter to discuss which solution is "best possible", though, as that would vary greatly on the application. If you're running a bank, you would never want to sacrifice consistency. If you're running a blog, availability and partition-resistance is probably more important.

> If you're running a bank, you would never want to sacrifice consistency.

Banks do sacrifice CAP consistency. As it doesn't mean you don't have consistency at all or anything like that. Just that you don't wait for writes to become visible to all nodes.

Proof by example or analogy is not a proof.

Sure — but, given the proof by contradiction, the examples would then illustrate the trade offs that the theorem forces.

This sounds wrong to me. Do visual proofs not count?

Proof by example can be a proof. It depends on the theorem statement.

Proove that you can walk. Walk. Prooved by an example. Basically to prove that something exists or that a property is not valid for every element of a set, you can proove with an example.

Proove that you can't walk. Don't walk.

Hmmmmmm.

Of course you can prove something exists by an example. And you can prove a property does not always hold with a counter example.

But if you want to prove that something doesn't exist, or a property always holds, then you shouldn't be looking for examples.

This is exactly what I've said. My initial "proof by example" was an answer for the op's statement:

> Proof by example or analogy is not a proof.

So as you also said "Of course you can prove something exists by an example".

To answer this: > Proove that you can't walk. Don't walk.

As I said, proof by example works only

> to prove that something exists or that a property is not valid for every element of a set.

Divide your lifetime in seconds. With that, you're trying to proove with the property "walk" isn't valid for every element of the set lifetime. To proove that the property can't walk dosen't hold for every element of the set, just show an example of second while you were walking and you're done.

The reverse proves something different. If you walk, you've proved that you CAN walk. Not walking is not a proof for lack of ability. It does however give a possible counter example to the assumption "If you can walk, you will walk"

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