Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 10, 2021 at 9:10 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
formatting
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| Aug 1, 2019 at 17:06 | comment | added | Duchamp Gérard H. E. | @ good hint (+1) | |
| Aug 1, 2019 at 10:33 | comment | added | Pietro Majer | In fact, a commonly neglected fact is that the representation of an element $x$ of a Hilbert space as sum of its Fourier components in a Hilbert basis $\{u_\lambda\}_{\lambda\in\Lambda}$, namely $x=\sum_{\lambda\in\Lambda} (x\cdot u_\lambda)u_\lambda$, is always a summable family in $H$. Recalling this, the above false belief would just reduce to the very false "$\ell_1(\Lambda)=\ell_2(\Lambda)$" for any set $\Lambda$, that hopefully not many believe! | |
| Feb 17, 2018 at 8:03 | comment | added | Duchamp Gérard H. E. | @RobertFurber Thank you for this learned description (+1) | |
| Feb 17, 2018 at 7:44 | comment | added | Robert Furber | I particularly like Grothendieck's version of this. He proves that unconditional convergence is the same as absolute convergence for a locally convex space if and only if it is nuclear, i.e. every continuous linear map to a normed space is a nuclear map. The falsity of this belief then follows from the fact that a nuclear normed space is finite dimensional. | |
| Dec 21, 2017 at 6:22 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
MathJax - the question has been bumped anyway
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| Sep 20, 2017 at 3:41 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Put "commutatively convergent" and "summable" withhin the text
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| Aug 9, 2017 at 2:02 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Completed the answer
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| Aug 7, 2017 at 22:42 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Recalled the definition of a summable family
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| Aug 7, 2017 at 19:26 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
MathJax: \|
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| Aug 7, 2017 at 18:25 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Formatting
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| S Aug 7, 2017 at 15:44 | history | answered | Duchamp Gérard H. E. | CC BY-SA 3.0 | |
| S Aug 7, 2017 at 15:44 | history | made wiki | Post Made Community Wiki by Duchamp Gérard H. E. |