Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18, 2015 at 9:35 | comment | added | bof | @Qiaochu: I thought the correct generalization of$$\operatorname{lcm}(a,b)=\frac{a\cdot b}{\operatorname{gcd}(a,b)}$$was $$\operatorname{lcm}(a,b,c)=\frac{a\cdot b\cdot c\cdot \operatorname{gcd}(a,b,c)}{\operatorname{gcd}(a,b)\cdot \operatorname{gcd}(a,c)\cdot \operatorname{gcd}(b,c)}$$Another false belief I guess. Maybe not a common one. | |
| May 21, 2011 at 6:25 | comment | added | Unknown | though the product is not necessarily $abc$, but it can be made so. | |
| May 21, 2011 at 6:24 | comment | added | Unknown | @Qiaochu, glad to see that. We do have more concerning generalisations to three variables: $$gcd(lcm(a,b),lcm(a,c),lcm(b,c))=lcm(gcd(a,b),gcd(a,c),gcd(b,c))$$ $$gcd(a, lcm(b,c)) = lcm(gcd(a,b),gcd(a,c))$$ $$lcm(a, gcd(b,c)) = gcd(lcm(a,b),lcm(a,c))$$ | |
| May 8, 2011 at 23:47 | comment | added | Qiaochu Yuan | @Elohemahab: actually, the correct generalization is $\gcd(a, b, c) \text{lcm}(ab, bc, ca) = \text{lcm}(a, b, c) \gcd(ab, bc, ca) = abc$. | |
| Feb 24, 2011 at 22:05 | comment | added | Unknown | @Qiaochu, that is a nice quick check. Let the RCF(remnant common factor) be the leftover factor that would make the above second equality true. There seems to be no interesting way of determining $RCF\left(a,b,c\right)$ so that $LCM\left(a,b,c\right)\times RCF\left(a,b,c\right) \times GCF\left(a,b,c\right) = abc$ | |
| Feb 24, 2011 at 21:08 | comment | added | Qiaochu Yuan | This kind of stuff is easy to rule out, though; it's dimensionally inconsistent. Replacing a, b, c by ka, kb, kc leads to a quick contradiction. | |
| Nov 29, 2010 at 6:46 | comment | added | Unknown | Yes. GCF means the same: Greatest Common Factor. | |
| Nov 27, 2010 at 19:33 | comment | added | Zsbán Ambrus | Does GCF mean gcd (greatest common divisor) here? | |
| Nov 27, 2010 at 14:23 | history | answered | Unknown | CC BY-SA 2.5 |