Totally agree with this post...however, to be extremely pedantic (and thus not suitable for the article in question), a tuple in the foundations of mathematics is typically defined as a set. That is, (x,y) := {x,{x,y}}, where the latter is the set containing the element x and the set {x,y}. That is how one goes from axiomatic set theory to define tuples of numbers.
There is a big difference between your type of pedantry versus the OP... I don't think the OP was pedantic. It is simply not a set of real numbers. He did say that it was a "small mistake".
The first is more an error of understanding (for the lack of a better term), whereas talking about tuples as being de facto sets is truly about being pedantic.
Absolutely! In this sense you are absolutely right, but a reader who knows how to construct such tuples (i.e. fill in the blanks in the article) also in all likelihood knows the content of the article. And I bet readers who don't know that already, will not realize that those are the sets the author means.
After stumbling across the author's twitter where he already complains that people are "being mean on HN", and seeing his responses there, I have some serious doubts about whether he is fit to be teaching people mathematics. I honestly applaud him for writing the article, and don't hold the math mistake against him at all. But the incredible defensiveness when confronted with a small mistake is absurd.
Who goes from axiomatic set theory at all, if their goal is not to be a logician/type theorist? One does not need to know axiomatic set theory to study linear algebra any more than one needs to know about semiconductors in order to program in Python.
To be even more pointlessly pedantic: sure, but that doesn't give you "sets of real numbers", in the sense of sets where every element can meaningfully be interpreted as a real number.
