Timeline for Nonequivalent definitions in Mathematics
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2023 at 3:23 | comment | added | Michael Renardy | I was once told that in Romanian afina means blueberry, and undergraduates always wonder why people talk about blueberry spaces and blueberry mappings. | |
| Aug 14, 2019 at 17:24 | comment | added | Francois Ziegler | Possible culprit Bourbaki, in La Tribu Nº 6 (1941): “adopted: Linear function (for “linear and homogeneous”); Affine function (for “linear (non homogeneous)”).” Borel (2001, p. xi) emphasizes: $𝐆𝐋_𝑛(𝑘)$ and $𝐒𝐋_𝑛(𝑘)$ are for us “the general and special linear groups, but this is not Lie’s terminology. For him, they are the general and special homogeneous linear groups. He reserves the term general linear group for our affine group $\textrm{Aff}(𝑘^𝑛)$”. | |
| Jun 15, 2019 at 10:01 | comment | added | Nicola Arcozzi | Something I have problems with when teaching Calculus II is this: if I call "tangent plane" the one physically tangent to the surface $S$ at $P$, how do I call the space of vectors tangent to $S$ to $P$? I call it "vector space tangent to $S$ at $P$", and I spend time to tell why the two objects are distinct, but closely related, but I'm not especially happy about this choice. | |
| Jan 22, 2018 at 22:16 | comment | added | Pietro Majer | An ODE $\dot u=Au+b$ is still called a "linear equation", and $\dot u=Au$ "linear homogeneous" | |
| Dec 20, 2017 at 17:08 | comment | added | Adam P. Goucher | @EricLippert Computer scientists would also call $n + \log{n}$ 'linear', even though it's not even affine. | |
| Nov 28, 2017 at 5:14 | comment | added | Joshua Grochow | @EricLippert: Although in CS there is never really any confusion about this. If we want to specify, we might say "linear growth rate." Also, sometimes we do talk about linear functions (lookup, e.g., "matrix rigidity"), and sometimes we talk about affine functions, and have to be careful about the distinction between the two. | |
| Nov 26, 2017 at 20:54 | comment | added | Michael | @EricLippert, similarly "exponential" in CS often refers to exp(polynomial), where polynomial doesn't have to be linear. | |
| Nov 24, 2017 at 16:35 | comment | added | Eric Duminil | @EricLippert: They're only interested in the asymptotic behaviour when $x$ gets to infinity. That's why $b$ is ignored. The number and speed of CPU is arbitrary, so $a$ is set to $1$. | |
| Nov 24, 2017 at 15:37 | comment | added | Eric Lippert | Computer science also uses "linear" to mean "cost grows directly proportional to problem size, ignoring a constant fixed cost", which is affine. | |
| Nov 23, 2017 at 8:40 | comment | added | Alex Jones | I teach my algebra students the term affine, but let them know that in most cases they are called "linear" despite not actually being linear. | |
| Nov 23, 2017 at 3:11 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Nov 23, 2017 at 0:40 | history | answered | Ari Brodsky | CC BY-SA 3.0 |