Is this question considered to be on-topic?
To me it seems to be asking about the meaning of English phrases in the context of mathematics, or alternatively about how to judge the validity of a mathematics research paper. Neither of these seem to me to be about maths education.
this question (if properly asked) has the educational benefit of dealing with that pernicious belief
doesn't seem very relevant to me, as my understanding was that this site was for asking about how to educate people in maths, not for doing the education.
On the other hand, at least 4 users think this is a good question.
Thus I am curious about what others think of this question.