xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 1 day agoImaginary numbers are more real than infinity.message-squaremessage-square33fedilinkarrow-up184arrow-down115
arrow-up169arrow-down1message-squareImaginary numbers are more real than infinity.xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 1 day agomessage-square33fedilink
minus-squarexia@lemmy.sdf.orgOPlinkfedilinkEnglisharrow-up2·11 hours agoDoes this mean the concept of infinity requires an infinite number of infinities?
minus-squareLeate_Wonceslace@lemmy.dbzer0.comlinkfedilinkEnglisharrow-up2·2 hours agoInformally, yes. Formally, no. There is no cardinal sufficient such that every cardinal can fit in a set with that cardinality. Isn’t that fascinating? There’s too many infinities for us to mathematically express how many infinities there are.
minus-squarePeriodicallyPedantic@lemmy.calinkfedilinkarrow-up1·9 hours agoI believe so. I wonder what is the ordinal of the set of ordinals.
Does this mean the concept of infinity requires an infinite number of infinities?
Informally, yes. Formally, no. There is no cardinal sufficient such that every cardinal can fit in a set with that cardinality. Isn’t that fascinating? There’s too many infinities for us to mathematically express how many infinities there are.
I believe so. I wonder what is the ordinal of the set of ordinals.