▲ 287 ▼ EDIT: I THINK I STAND CORRECTED (lemmy.zip) submitted 2 years ago* (last edited 2 years ago) by balderdash9@lemmy.zip to c/memes@lemmy.world 218 comments fedilink hide all child comments I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
[–] ferralcat@monyet.cc 10 points 2 years ago (3 children) An infinite number of bills would mean there's no space to move or breathe in, right? We'd all suffocate or be crushed under the pressure? permalink fedilink source hideshow 6 child comments replies: [–] Natanael@slrpnk.net 5 points 2 years ago Depends on implementation. There's a hierarchy called cardinality, and any two infinitives that can be cleanly mapped 1:1 are considered equal even if one "looks" bigger, like in the example from OP where you can map 100x 1 dollar bills to each 100 dollar bill into infinity and not encounter any "unmappable" units, etc. So filling an infinite 3D volume with paper bills is practically equivalent to filling a line within the volume, because you can map an infinite line onto a growing spiral or cube where you keep adding more units to fill one surface. If you OTOH assumed bills with zero thickness you can have some fun with cardinalities and have different sized of infinities! permalink fedilink source parent [–] Duke_Nukem_1990@feddit.de 2 points 2 years ago We'd all suffocate or be crushed under the pressure? hey just like regular capitalism permalink fedilink source parent [–] ferralcat@monyet.cc 1 point 2 years ago I guess you'd need infinite space for an infinite number of bills. But it'd still be full to the brim? permalink fedilink source parent
[–] Natanael@slrpnk.net 5 points 2 years ago Depends on implementation. There's a hierarchy called cardinality, and any two infinitives that can be cleanly mapped 1:1 are considered equal even if one "looks" bigger, like in the example from OP where you can map 100x 1 dollar bills to each 100 dollar bill into infinity and not encounter any "unmappable" units, etc. So filling an infinite 3D volume with paper bills is practically equivalent to filling a line within the volume, because you can map an infinite line onto a growing spiral or cube where you keep adding more units to fill one surface. If you OTOH assumed bills with zero thickness you can have some fun with cardinalities and have different sized of infinities! permalink fedilink source parent
[–] Duke_Nukem_1990@feddit.de 2 points 2 years ago We'd all suffocate or be crushed under the pressure? hey just like regular capitalism permalink fedilink source parent
[–] ferralcat@monyet.cc 1 point 2 years ago I guess you'd need infinite space for an infinite number of bills. But it'd still be full to the brim? permalink fedilink source parent
