Talk:2042: Rolle's Theorem - Revision history

42.book.addict at 20:19, 24 November 2025

2025-11-24T20:19:37Z

42.book.addict at 20:18, 24 November 2025

2025-11-24T20:18:40Z

Artem: Added comment,

2025-11-23T06:35:17Z

Added comment,

Firestar233 at 03:08, 25 September 2024

2024-09-25T03:08:36Z

172.69.151.94 at 09:06, 14 October 2023

2023-10-14T09:06:54Z

172.69.151.93 at 09:03, 14 October 2023

2023-10-14T09:03:41Z

141.101.99.238: Tyop.

2022-08-01T18:53:27Z

Tyop.

141.101.99.238: A bit more context, and an awful pun...

2022-08-01T18:52:43Z

A bit more context, and an awful pun...

172.70.91.128 at 18:36, 1 August 2022

2022-08-01T18:36:42Z

162.158.159.133 at 18:23, 1 August 2022

2022-08-01T18:23:40Z

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 :TAN(x) isn't differentiable at pi/2, hence the theorem doesn't apply--[[Special:Contributions/162.158.92.40|162.158.92.40]] 07:48, 6 September 2018 (UTC)
 ::And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 08:01, 6 September 2018 (UTC)
-:::Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. Zetfr 09:17, 6 September 2018 (UTC)
+:::Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. {{unsigned|Zetfr}} 09:17, 6 September 2018 (UTC)
 '''Clueless Museum Visitor'''
-The math in the comic is well explained, but shouldn't there be something about the "math equivalent of the clueless art museum visitor..." part? Zetfr 09:17, 6 September 2018 (UTC)
+The math in the comic is well explained, but shouldn't there be something about the "math equivalent of the clueless art museum visitor..." part? {{unsigned|Zetfr}} 09:17, 6 September 2018 (UTC)
 : Seconded, all the argument here is about math that isn't even *in* the comic, whereas the bit that confuses me is the cultural metaphor... [[Special:Contributions/162.158.154.235|162.158.154.235]] 07:16, 7 September 2018 (UTC)
 : I had a go.[[Special:Contributions/162.158.154.103|162.158.154.103]] 08:35, 7 September 2018 (UTC)

@@ Line 1: / Line 1: @@
 <!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.-->
 Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. [[Special:Contributions/172.69.54.165|172.69.54.165]] 15:51, 5 September 2018 (UTC)
 :Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)
@@ Line 22: / Line 21: @@
 * From {{w|Thales|Wikipedia}}: Other quotes from Proclus list more of Thales' mathematical achievements: "They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre." [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:39, 6 September 2018 (UTC)
 * On the other hand not all historian believe Proclus. But van der Waerden does: [https://books.google.com/books?id=HK3vCAAAQBAJ&pg=PA88#v=onepage&q&f=false]. [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:49, 6 September 2018 (UTC)
 '''Rolle's Theorem counterexample?'''
@@ Line 30: / Line 28: @@
 ::And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 08:01, 6 September 2018 (UTC)
 :::Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. Zetfr 09:17, 6 September 2018 (UTC)
 '''Clueless Museum Visitor'''
@@ Line 38: / Line 34: @@
 : Seconded, all the argument here is about math that isn't even *in* the comic, whereas the bit that confuses me is the cultural metaphor... [[Special:Contributions/162.158.154.235|162.158.154.235]] 07:16, 7 September 2018 (UTC)
 : I had a go.[[Special:Contributions/162.158.154.103|162.158.154.103]] 08:35, 7 September 2018 (UTC)
 Just so we're on the same page, while the proof of Rolle's theorem is not completely trivial, neither is it difficult by any means. Proving it seems to be a pretty common homework assignment in undergrad math classes, for example, so one might legitimately ask why it deserved to be named. Perhaps it's simply that it's old enough that the methods at the time were crappy, and so modern proofs are much easier. [[Special:Contributions/172.69.22.140|172.69.22.140]]
@@ Line 63: / Line 58: @@
 :::: You seem to be missing what I am referring to. There are at least two parts. Let's start with the main one. You keep referring to the same place of the same article. That is not under contention, so it is irrelevant. So I checked Wikipedia's article on FTC itself and I think I see why you don't see my point. When I learnt FTC from textbooks, the definition of integrals is via the area under curve, i.e. the relevant bit in the FTC article is the geometric intuition. The FTC article, however, quite much like you seem to be, however, only covers the anti-derivative part. In a sense, it comes down to the definition of what an ``integral" means. AFAIK, for beginners, there is only 3 definitions in common use, the directed area under curve, limit of a certain sum, and anti-derivatives. When I teach, I tend to define the directed area under curve, just because students like to see things. Because of that, my FTC has to cover the area under curve. And that is the 2D integral known to Leibniz. If you want the 2D integral, then you ought to integrate the fundamental differential form I was talking about---you don't talk about generalised Stokes's theorem without differential geometry, and I am trying to say that the identification of a definite integral with the area under curve is what is taught to beginning students, but is highly non-trivial under differential geometry! I hope this is clearer. Of course, the moment the 2D integral is reduced to a 1D integral with new boundaries, then the part you keep referring to is relevant, and again, not under any contention. I am simply saying I am not happy with that being the sole content of FTC. The FTC I respect is the one that includes the geometrical intuition. Finally, just the quibble---what part of my ``the restricted FTC is a consequence of generalised Stokes's theorem" is different from your ``FTC restricted to smooth functions is simply a special case of Stokes' theorem"? Even if you disagreed with my ``applied twice", you should not be disagreeing with my ``basically what I said". [[Special:Contributions/162.158.166.191|162.158.166.191]] 16:55, 10 September 2018 (UTC)
-"Munroe's theorem" should definitely refer to the circle thing in the alt text {{unsigned ip|162.158.62.57}}
+"Munroe's theorem" should definitely refer to the circle thing in the alt text {{unsigned ip|162.158.62.57|02:05, 7 September 2018 (UTC)}}
 Since I'm half a mathematician, I did the math. I looked up Rolle's theorem and it uses the theorem of Weierstraß. I looked up the theorem of Weierstraß (better known as extreme value theorem) and it uses the theorem of Bolzano-Weierstraß. I looked up...why am I suddenly reminded of https://xkcd.com/609 ? :-) [[Special:Contributions/141.101.104.71|141.101.104.71]] 08:36, 7 September 2018 (UTC)
 What goes up must come down. [[Special:Contributions/198.41.238.64|198.41.238.64]] 05:53, 8 September 2018 (UTC)
 '''Going in the opposite direction.'''
 Sure, some seemingly obvious things can be made theorems, but there's a point of view that the most complex theorems may seem obvious to a sufficiently smart entity, that we have such hard time studying mathematics simply because it's difficult for us to grasp long sequences of obvious connections in our insufficiently powerful imagination, so we need to break it down into manageable pieces.
-"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957) {{unsigned ip|162.158.74.231}}
+"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957) {{unsigned ip|162.158.74.231|06:39, 11 September 2018 (UTC)}}
 "This is what f'(c) = 0 means, as f' is a common notation for the derivative of the function f in differential calculus." Is it? I took both calculus and differential equations as an undergraduate (in the United States in the 1970s/1980s) and never saw that notation.[[User:Nitpicking|Nitpicking]] ([[User talk:Nitpicking|talk]]) 17:57, 1 August 2022 (UTC)

@@ Line 4: / Line 4: @@
 :Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)
 ::Which article? [https://en.wikipedia.org/wiki/Special:Log?type=&user=&page=Munroes+theorem&wpdate=&tagfilter=&wpFormIdentifier=logeventslist The log] is empty --[[Special:Contributions/172.69.151.94|172.69.151.94]] 09:06, 14 October 2023 (UTC)
 :Proposed ideas for Munroe's Law:

@@ Line 14: / Line 14: @@
 ::Proposed idea for Munroe[[wikipedia:Apostrophe#Smart quotes|’]]<nowiki/>s Law:
 :::[[wikipedia:Dash#Itemization mark|–]][[mw:Help:Lists| <nowiki/>]]Whenever XKCD references a theorem, an edit war is caused on the respective Wikipedia article.--[[Special:Contributions/172.69.151.93|172.69.151.93]] 09:03, 14 October 2023 (UTC)
 I feel like Euclid beat Randall to the punch here, a couple millennia. [[Special:Contributions/162.158.155.146|162.158.155.146]] 16:54, 5 September 2018 (UTC)

@@ Line 3: / Line 3: @@
 Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. [[Special:Contributions/172.69.54.165|172.69.54.165]] 15:51, 5 September 2018 (UTC)
 :Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)
 :Proposed ideas for Munroe's Law:
@@ Line 11: / Line 12: @@
 ::Done. [[User:Kmote|Kmote]] ([[User talk:Kmote|talk]]) 17:56, 10 September 2018 (UTC)
 ::Speaking of popular culture, there's a (moderately) well known Ballad of Rolle's theorem [https://www.youtube.com/watch?v=S0BXv90MlhA Balada o vete Rolleovej] ("moderately" meaning some people who studied at Faculty of mathematics in Bratislava might have heard (of) it) --[[User:Kventin|Kventin]] ([[User talk:Kventin|talk]]) 07:41, 7 September 2018 (UTC)
-::Proposed idea for Munroe[[wikipedia:Apostrophe#Smart quotes|’]]s Law:
+::Proposed idea for Munroe[[wikipedia:Apostrophe#Smart quotes|’]]<nowiki/>s Law:
 :::[[wikipedia:Dash#Itemization mark|–]][[mw:Help:Lists| <nowiki/>]]Whenever XKCD references a theorem, an edit war is caused on the respective Wikipedia article.--[[Special:Contributions/172.69.151.93|172.69.151.93]] 09:03, 14 October 2023 (UTC)

@@ Line 74: / Line 74: @@
 :Coming from a UK background, myself, I recognise it as such. Not really much experience the '70s, but definitely across the early '80s and beyond. For Secondary Education, in the first instance where the initial "Number machines" idea led straight into algebra, and differentiation/integration was in the second or third year (whatever that is in 'K-12'-style numbering that's in use today, seemingly imported from the US). Not sure what system dominated beyond secondary and tertiary/college levels and into my own university years (heading towards the '90s). It might have depended on whether it was the physics or the maths lectures and workshops (or indeed the given lecturer/workshopper of the moment) as to which of the many possible conventions we could have used and be considered correct. dFoo/dBar probably was used a lot, but obviously got messier than ''f''unctioning things when going far into that sort of thing (either direction!). Though whether curly-ds or primes, it does get more difficult to differentiate the number of differentiations once you get into higher realms of notation... ;)
 :I went a-looking and it ''is'' fairly common, even unto {{w|Derivative#Higher_derivatives|higher derivatives with multiple marks}} (which I've used, well... to no more than the third degree, probably).
-:Looking further still, I now know (have remindedvmyself?) that {{w|Notation for differentiation#Lagrange's notation|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into the numeric form rather than repeated Prime-marks towards a sublime ridiculousness.
+:Looking further still, I now know (have reminded myself?) that {{w|Notation for differentiation#Lagrange's notation|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into the numeric form rather than repeated Prime-marks towards a sublime ridiculousness.
 :Of course, elsewhere on that latter link you might find your own learnt system. Or various others more familiar to you and which I ''may'' as readily recognise, unprompted. [[Special:Contributions/162.158.159.133|162.158.159.133]] 18:23, 1 August 2022 (UTC)

@@ Line 72: / Line 72: @@
 "This is what f'(c) = 0 means, as f' is a common notation for the derivative of the function f in differential calculus." Is it? I took both calculus and differential equations as an undergraduate (in the United States in the 1970s/1980s) and never saw that notation.[[User:Nitpicking|Nitpicking]] ([[User talk:Nitpicking|talk]]) 17:57, 1 August 2022 (UTC)
-:Coming from a UK background (and not really much in the '70s, but definitely across the early '80s and beyond) I recognise it. I went a-looking and it is fairly common, even unto {{w|Derivative#Higher_derivatives|higher derivatives with multiple marks}} (which I've used, well... to no more than the third degree, probably).
+:Coming from a UK background, myself, I recognise it as such. Not really much experience the '70s, but definitely across the early '80s and beyond. For Secondary Education, in the first instance. Not sure what system dominated beyond secondary and tertiary/college levels and into my own university years (heading towards the '90s). It might have depended on whether it was the physics or the maths lectures and workshops (or indeed the given lecturer/workshopper of the moment) as to which of the many possible conventions we could have used and be considered correct. dFoo/dBar probably was used a lot, but obviously got messier than ''f''unctioning things when going far into that sort of thing (either direction!)
-:Looking further still, {{w|Notation for differentiation#Lagrange's notation|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into numerals rather than repeated Prime-marks.
+:I went a-looking and it ''is'' fairly common, even unto {{w|Derivative#Higher_derivatives|higher derivatives with multiple marks}} (which I've used, well... to no more than the third degree, probably).
-:Elsewhere on that latter link you might find your own learnt system (or various others more familiar to you), of course. [[Special:Contributions/162.158.159.133|162.158.159.133]] 18:23, 1 August 2022 (UTC)
+:Looking further still, I now know (have remindedvmyself?) that {{w|Notation for differentiation#Lagrange's notation|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into the numeric form rather than repeated Prime-marks towards a sublime ridiculousness.

← Older revision		Revision as of 18:23, 1 August 2022
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	"This is what f'(c) = 0 means, as f' is a common notation for the derivative of the function f in differential calculus." Is it? I took both calculus and differential equations as an undergraduate (in the United States in the 1970s/1980s) and never saw that notation.[[User:Nitpicking\|Nitpicking]] ([[User talk:Nitpicking\|talk]]) 17:57, 1 August 2022 (UTC)		"This is what f'(c) = 0 means, as f' is a common notation for the derivative of the function f in differential calculus." Is it? I took both calculus and differential equations as an undergraduate (in the United States in the 1970s/1980s) and never saw that notation.[[User:Nitpicking\|Nitpicking]] ([[User talk:Nitpicking\|talk]]) 17:57, 1 August 2022 (UTC)
		+	:Coming from a UK background (and not really much in the '70s, but definitely across the early '80s and beyond) I recognise it. I went a-looking and it is fairly common, even unto {{w\|Derivative#Higher_derivatives\|higher derivatives with multiple marks}} (which I've used, well... to no more than the third degree, probably).
		+	:Looking further still, {{w\|Notation for differentiation#Lagrange's notation\|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into numerals rather than repeated Prime-marks.
		+	:Elsewhere on that latter link you might find your own learnt system (or various others more familiar to you), of course. [[Special:Contributions/162.158.159.133\|162.158.159.133]] 18:23, 1 August 2022 (UTC)