Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2017 at 13:22 | comment | added | Todd Trimble | It's mainly in agreement with you, with a shade of neutral. I don't claim that my suggestion really makes it easier, but only that one can prove things rigorously without getting into considerations of arc length, with (theoretically anyway) no prerequisites past introductory differential calculus. Mainly it's based on convexity arguments; I have a write-up here: ncatlab.org/toddtrimble/published/…; see theorem 3.1 and the crucial lemma 3.4. The "finesse" is akin to how we adjust parameter $a$ in $f: x \mapsto a^x$ to $a = e$ to get $f'(0) = 1$. | |
| Oct 10, 2017 at 11:56 | comment | added | Sebastien Palcoux | @ToddTrimble: Should we interpret your comment as for or against this false belief? Or else, is it just a neutral complement? For a full proof, is your way really easier? | |
| Oct 8, 2017 at 3:14 | comment | added | Todd Trimble | The string of comments below the Math.SE link shows that really pursuing this gets one down a rabbit hole of rigorous discussions of arc length and such. On the other hand, one can prove that if $S$ (think "sine") and $C$ (think "cosine") are continuous functions which satisfy the standard addition formulas and the Pythagorean theorem $C^2 + S^2 \equiv 1$, then $S'(0)$ exists and $S'(x) = S'(0)C(x)$. There is a whole family of sine-like functions $S_a: x \mapsto S(ax)$; adjusting the parameter $a$ so that $S_a^\prime(0) = 1$, you can define the standard sine to be this $S_a$: a neat finesse. | |
| Sep 21, 2017 at 16:27 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Addition of **False belief:**
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| Sep 16, 2017 at 12:16 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
added 57 characters in body
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| S Sep 16, 2017 at 12:07 | history | answered | Sebastien Palcoux | CC BY-SA 3.0 | |
| S Sep 16, 2017 at 12:07 | history | made wiki | Post Made Community Wiki by Sebastien Palcoux |