- #1

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- TL;DR Summary
- Pseudophilosophal question about a definition

Hi, PF, I've got a quote, and a philosophical question

Figure shown suggests that a function ##f(x)## can have local extreme values only at ##x## points of three special types:

(i)

(ii)

(iii)

And now my "brainstorm": (iii) is not defined as "reductio ad absurdum"; not "principle of exclusion".

My question: what kind of argument makes use of? I'm just overthinking? Why does talk about closed intervals in such a "implicit" (suggested, but not communicated directly) way?

PS: I'm not sure of the LaTeX used, and insecure about "Preview" tool, so I will click "Post thread". Please check. Thanks!

Figure shown suggests that a function ##f(x)## can have local extreme values only at ##x## points of three special types:

(i)

**Critical points**of ##f## (points ##x## in ##\mathfrak{D}(f)## where ##f'(x)=0##)(ii)

**Singular points**of ##f## (points ##x## in ##\mathfrak{D}(f)## where ##f'(x)## is not defined)(iii)

**Endpoints**of the domain of ##f## (points in ##\mathfrak{D}(f)## that do not belong to any open interval contained in ##\mathfrak{D}(f)##)And now my "brainstorm": (iii) is not defined as "reductio ad absurdum"; not "principle of exclusion".

My question: what kind of argument makes use of? I'm just overthinking? Why does talk about closed intervals in such a "implicit" (suggested, but not communicated directly) way?

PS: I'm not sure of the LaTeX used, and insecure about "Preview" tool, so I will click "Post thread". Please check. Thanks!