🧵 Geometry by Audin
Anonymous at Fri, 19 Jul 2024 03:32:45 UTC No. 16288027
Why does this function need to be partial? What element of the domain can't get mapped to a vector in the vector space E?
Anonymous at Fri, 19 Jul 2024 12:22:15 UTC No. 16288318
They call it partial because you've partially evaluated the previous function in one it's two arguments.
Also this book looks fucking terrible, Def. 1.1 is very obnoxiously phrased.
Anonymous at Fri, 19 Jul 2024 12:49:39 UTC No. 16288335
>>16288318
That is not the definition of a partial map
Anonymous at Fri, 19 Jul 2024 13:00:36 UTC No. 16288343
>>16288318
You must not be endowed.
Anonymous at Sat, 20 Jul 2024 03:57:44 UTC No. 16289215
>>16288318
can't be the case since the domain is different though
Anonymous at Sat, 20 Jul 2024 03:58:30 UTC No. 16289216
>homework thread
Anonymous at Sat, 20 Jul 2024 04:49:52 UTC No. 16289254
>>16288318
>Also this book looks fucking terrible, Def. 1.1 is very obnoxiously phrased
french
please understand
Anonymous at Sat, 20 Jul 2024 05:43:22 UTC No. 16289274
>>16288335
It's not, but it's clear from context that is what is intended.
>>16289215
Isn't that what you would expect here?
Anonymous at Sat, 20 Jul 2024 06:36:05 UTC No. 16289316
This doesn’t make sense: B is a point, not a subset of the vector space. The only thing I can think is that B is supposed to represent a subset of the vector space with only one element(that of B). If so, I think that they are saying the following: for a given point A, theta is the partial map from the aforementioned subset B to the vector for the codomain space. I think that it would be partial in this context because this subset only contains one point, B. Hope that this helps
Anonymous at Sat, 20 Jul 2024 18:50:11 UTC No. 16289919
>>16289316
>The only thing I can think is that B is supposed to represent a subset of the vector space
You meant affine space correct?
Anonymous at Sat, 20 Jul 2024 19:01:19 UTC No. 16289930
>>16289316
[math]A[/math] and [math]B[/math] are both points in the affine space. The domain of [math]\Theta_A[/math] is [math] \mathcal{E}[/math] and the codomain is [math]E[/math].
[eqn]\Theta_A(B) = \Theta(A,B) = \overrightarrow{AB}[/eqn]
Anonymous at Sat, 20 Jul 2024 19:09:45 UTC No. 16289942
>>16289930
How is Theta A a partial map instead of a total map?
Anonymous at Sat, 20 Jul 2024 19:36:46 UTC No. 16289969
>>16289942
Perhaps because ThetaA(A) is not defined?
Anonymous at Sat, 20 Jul 2024 20:04:40 UTC No. 16290003
>>16289930
>>16289969
Okay smart pants, now explain why we have the condition for all A but not for all B in the partial map Theta(A) from the affine space to the vector space.
Anonymous at Sat, 20 Jul 2024 20:28:58 UTC No. 16290037
>>16290003
You have a map theta such that for any pair of points A, B in epsilon we have that theta(A,B) = vector AB in E. So that is why theta_A doesn't need to repeat for all B again. Now, the partial map here means partial application, that is your two variable functions has already one variable fixed, A, such that result in a funciton of one variable:
"In computer science, partial application (or partial function application) refers to the process of fixing a number of arguments of a function, producing another function of smaller arity"
Anonymous at Sat, 20 Jul 2024 20:32:24 UTC No. 16290040
>>16290037
So it's all sloppy writing, thanks anon.
Anonymous at Sun, 21 Jul 2024 02:27:44 UTC No. 16290343
nigger book
Anonymous at Sun, 21 Jul 2024 06:11:24 UTC No. 16290495
>>16290378
Sounds quite appropriate for an elementary geometry textbook aimed at mathematics students and mathematicians vs high schoolers.
Anonymous at Mon, 22 Jul 2024 00:39:09 UTC No. 16291674
>>16290495
it's not, elementary geometry should have no prerequisites
Anonymous at Mon, 22 Jul 2024 09:37:31 UTC No. 16291935
>>16291674
I quite like that there are works like Audin's that put elementary geometry in the context of modern mathematics.