upquark

> Nowadays, my primary criteria for joining a team is the quality of the people and of the manager.

That's mine too, but nowadays teams and especially managers last about 6 months in one place. What is one supposed to do?

Totally a preference thing. I strongly prefer pandas to dplyr having worked with both.

How much of success is luck? I honestly don't know. It feels like another feel-good mantra coming out of SV culture. Most successful people I know or have heard of do not fit the profile of an average Joe (including qualities that are pre-set at birth and cannot change with success).

What makes reddit and now HN think Ataturk was some sort of beacon of democracy?

> In January 1920, Mustafa Kemal advanced his troops into Marash where the Battle of Marash ensued against the French Armenian Legion. The battle resulted in a Turkish victory alongside the massacres of 5,000–12,000 Armenians spelling the end of the remaining Armenian population in the region.

He finished off the Cilician Armenians from Anatolia, whoever was left under French protection and had escaped the Genocide.

> Defining the set of real numbers is very different from defining all real numbers.

I'm saying that ^ sentence makes no sense to me, I don't know how to parse it formally. If you start talking about the set of "definable" numbers (not computable, but specifically "definable"), I believe you're gonna run into paradoxes as it's an ill-defined concept, similar (in spirit) to "all integers described under 100 words". In fact, the linked article actually talks about it in 2.3.

> For any given language, like for instance ZFC, we can say that definable numbers are a countable subset. Hence measure zero.

If I can describe a set of objects, then we're all set as far as I'm concerned (mathematically speaking). Being able to efficiently construct individual elements of this set using Turing machines or other computational devices is an orthogonal problem.

Also, I don't think having only countable number of utterances in ZFC precludes you from having well-defined uncountable sets described in that system (quite obviously, for any set S take 2^S which is very well-defined).

No, my "ill-defined" means "will lead to contradictions if you look too closely", not "I haven't exactly specified what it means".

Yes but you defined the number just fine, right? "Compute" is a separate issue from "define", you can't compute a lot of things. Is this going in the intuitionistic logic direction?

Still not sure I follow. Set of non-kings is not ill-defined, not in the same way as set of numbers non-describable by any formal system is.

My example is incomplete, not faulty. I left it as a question (does the inf belong to the set?). If the answer is yes, we reached a contradiction. If the answer is no, we have to continue further zooming in to this interval (or some other construction along those lines).

See, I claim that this set is ill-defined, so I can't know its properties like whether or not it's dense, open, closed, Borel-measurable, etc. etc.

You have to tell me what its properties are, and I will come up with a concrete proof that the set in question is ill-defined.

EDIT: After I RTFA'd, this is actually the paradox in section 2.3 of the linked article

Wait, you're agreeing with me that the set in question is ill-defined, but still somehow comparable to other sets? I am not sure I follow. My statement is that you cannot meaningfully talk about "all the numbers that cannot be described with language". If you could, I'd ask you if this set intersected with [0, 1] has a lower bound / 'inf' that's contained in it, and if so, did I just describe that lower bound with language? I'm sure some sort of paradox similar to the one with integers can be constructed here...

In my view, every real number is well-defined and there's nothing controversial about the set of real numbers. If the infinite aspect of it causes some researchers to call it a "mathematical fantasy", so be it, so is literally every other mathematical model we use in our lives.