xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 10 days agoImaginary numbers are more real than infinity.message-squaremessage-square44fedilinkarrow-up196arrow-down118
arrow-up178arrow-down1message-squareImaginary numbers are more real than infinity.xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 10 days agomessage-square44fedilink
minus-squarexia@lemmy.sdf.orgOPlinkfedilinkEnglisharrow-up3·9 days agoDoes this mean the concept of infinity requires an infinite number of infinities?
minus-squareLeate_Wonceslace@lemmy.dbzer0.comlinkfedilinkEnglisharrow-up4arrow-down1·9 days 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 days 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.