this post was submitted on 28 Apr 2024
503 points (96.8% liked)
Science Memes
11047 readers
3445 users here now
Welcome to c/science_memes @ Mander.xyz!
A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
- Don't throw mud. Behave like an intellectual and remember the human.
- Keep it rooted (on topic).
- No spam.
- Infographics welcome, get schooled.
This is a science community. We use the Dawkins definition of meme.
Research Committee
Other Mander Communities
Science and Research
Biology and Life Sciences
- !abiogenesis@mander.xyz
- !animal-behavior@mander.xyz
- !anthropology@mander.xyz
- !arachnology@mander.xyz
- !balconygardening@slrpnk.net
- !biodiversity@mander.xyz
- !biology@mander.xyz
- !biophysics@mander.xyz
- !botany@mander.xyz
- !ecology@mander.xyz
- !entomology@mander.xyz
- !fermentation@mander.xyz
- !herpetology@mander.xyz
- !houseplants@mander.xyz
- !medicine@mander.xyz
- !microscopy@mander.xyz
- !mycology@mander.xyz
- !nudibranchs@mander.xyz
- !nutrition@mander.xyz
- !palaeoecology@mander.xyz
- !palaeontology@mander.xyz
- !photosynthesis@mander.xyz
- !plantid@mander.xyz
- !plants@mander.xyz
- !reptiles and amphibians@mander.xyz
Physical Sciences
- !astronomy@mander.xyz
- !chemistry@mander.xyz
- !earthscience@mander.xyz
- !geography@mander.xyz
- !geospatial@mander.xyz
- !nuclear@mander.xyz
- !physics@mander.xyz
- !quantum-computing@mander.xyz
- !spectroscopy@mander.xyz
Humanities and Social Sciences
Practical and Applied Sciences
- !exercise-and sports-science@mander.xyz
- !gardening@mander.xyz
- !self sufficiency@mander.xyz
- !soilscience@slrpnk.net
- !terrariums@mander.xyz
- !timelapse@mander.xyz
Memes
Miscellaneous
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
A vector is a list of numbers, at its most basic. You can add a lot of extra functionality to it, but at its core, its just a list.
Functions from the reals to the reals are an example of a vector space with elements which can not be represented as a list of numbers.
It still can be, just not on infinite precision as nothing can with fp.
But the vector space of (all) real functions is a completely different beast from the space of computable functions on finite-precision numbers. If you restrict the equality of these functions to their extension,
defined as f = g iff forall x\in R: f(x)=g(x),
then that vector space appears to be not only finite dimensional, but in fact finite. Otherwise you probably get a countably infinite dimensional vector space indexed by lambda terms (or whatever formalism you prefer.) But nothing like the space which contains vectors like
F_{x_0}(x) := (1 if x = x_0; 0 otherwise)
where x_0 is uncomputable.