Science Memes

11004 readers

1993 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

!spiders@lemmy.world

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

Sal@mander.xyz

fossilesque@mander.xyz

SciBot@mander.xyz

491

Explain yourselves, comp sci. (mander.xyz)

submitted 6 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

62 comments fedilink hide all child comments

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

[–] GnomeKat@lemmy.blahaj.zone 4 points 6 months ago (1 children)

Its the algebraic properties that are important, not all vectors are n-tuples, eg the set of polynomials of degree less than n.

You need a basis to coordinate a vector, you can work with vectors without doing that and just deal with the algebraic properties. The coordinate representation is dependent on the basis chosen and isn't fundamental to the vector. So calling them n-tuples isn't technically correct.

You can turn them into a set of coordinates if you have a basis, but the fact that you can do that is because of the algebraic properties so it's those properties which define what a vector is.

[–] Leate_Wonceslace@lemmy.dbzer0.com 0 points 6 months ago* (last edited 6 months ago)

I think a better example to show how vectors don't necessarily need to be what people conceptualize as n-tuples would have been the real numbers. (Of course, these can be considered 1-tuples, but the same can be said of any arbitrary set element that is not itself a tuple with more entries.) A cooler example would have been R[x] (the ring of real-valued polynomials of a single variable) especially since an isomorphic ring using n-tuples would be a more cumbersome representation of the algebra.