fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 2 days agoListen here, Little Dickymander.xyzimagemessage-square51fedilinkarrow-up1404arrow-down15
arrow-up1399arrow-down1imageListen here, Little Dickymander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 2 days agomessage-square51fedilink
minus-squaregandalf_der_12te@discuss.tchncs.delinkfedilinkEnglisharrow-up3·edit-224 hours agofun fact: the vector space of differentiable functions (at least on compact domains) is actually of countable dimension. still infinite though
minus-squareiAvicenna@lemmy.worldlinkfedilinkEnglisharrow-up1·edit-220 hours agoDoesn’t BCT imply that infinite dimensional Banach spaces cannot have a countable basis
minus-squaregandalf_der_12te@discuss.tchncs.delinkfedilinkEnglisharrow-up1·edit-21 hour agoUhm, yeah, but there’s two different definitions of basis iirc. And i’m using the analytical definition here; you’re talking about the linear algebra definition.
fun fact: the vector space of differentiable functions (at least on compact domains) is actually of countable dimension.
still infinite though
Doesn’t BCT imply that infinite dimensional Banach spaces cannot have a countable basis
Uhm, yeah, but there’s two different definitions of basis iirc. And i’m using the analytical definition here; you’re talking about the linear algebra definition.