xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 8 个月前Imaginary numbers are more real than infinity.message-squaremessage-square43fedilinkarrow-up185arrow-down115
arrow-up170arrow-down1message-squareImaginary numbers are more real than infinity.xia@lemmy.sdf.org to Showerthoughts@lemmy.worldEnglish · 8 个月前message-square43fedilink
minus-squarexia@lemmy.sdf.orgOPlinkfedilinkEnglisharrow-up3·8 个月前Does this mean the concept of infinity requires an infinite number of infinities?
minus-squareLeate_Wonceslace@lemmy.dbzer0.comlinkfedilinkEnglisharrow-up3·8 个月前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.
minus-squarePeriodicallyPedantic@lemmy.calinkfedilinkarrow-up1·8 个月前I believe so. I wonder what is the ordinal of the set of ordinals.
Which infinity?
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.