Science Memes

10963 readers

2389 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

[email protected]

Other Mander Communities

Science and Research

Biology and Life Sciences

Physical Sciences

Humanities and Social Sciences

Practical and Applied Sciences

Memes

Miscellaneous

founded 2 years ago

MODERATORS

[email protected]

503

Explain yourselves, comp sci. (mander.xyz)

submitted 6 months ago by [email protected] to c/[email protected]

71 comments fedilink hide all child comments

you are viewing a single comment's thread
view the rest of the comments

[–] [email protected] 4 points 6 months ago (1 children)

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.

[–] [email protected] 0 points 6 months ago* (last edited 6 months ago) (1 children)

It still can be, just not on infinite precision as nothing can with fp.

[–] [email protected] 3 points 6 months ago* (last edited 6 months ago)

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.