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What means the term "under scrutiny" in mathematics?

I am not a native speaker but I understand that that "under scrutiny" means something like "being watched closely" in general meaning.

As far as I understand "under scrutiny" in mathematics and other sciences means "exploring extreme and rare conditions". For example, one may teach high school students that a rational function may not be defined for some X values or that an optimization algorithm maybe stuck in local maximum under certain rare conditions. Is that correct?

Carol Eisen
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    I think this is not related to mathematics in particular, see here. – Dietrich Burde Apr 02 '17 at 19:59
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    Any term depends on its context. What is the text where you are seeing this phrase? What is the surrounding sentence, paragraph, etc.? – Zev Chonoles Apr 02 '17 at 20:03
  • I have read it several times.Today I read: recurrent "Markov chains can be transient within the iterations under scrutiny" and may drift off. – Carol Eisen Apr 02 '17 at 20:09
  • Welcome to math stack exchange! I found it at Saibians large-number-page : The claim that Andre Joyce beats the large numbers of Jonathan Bowers does not hold "under scrutiny". – Peter Apr 02 '17 at 20:13
  • For those who want to know it exactly : Link : https://sites.google.com/site/largenumbers/home/3-2/andre_joyce Sentence : "As you can see this claim does not hold under scrutiny." – Peter Apr 02 '17 at 20:17
  • Given this link, it is quite clear that Saibian does not have in mind "pathological cases", but simply means that carefully checking reveals the fallacy. So, in this context the words mean something like : "Under careful verification" – Peter Apr 02 '17 at 20:23
  • I can accept that. Every thorough investigation will also deal with unlikely but possible scenarios. Thanks for the quick replies! – Carol Eisen Apr 02 '17 at 20:26
  • Probably english.stackexchange or linguistics or some similar site would fit better. – mathreadler Apr 02 '17 at 20:45

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