Each number is represented as a circle which contains the numbers below it.
4 contains 1 2 3 and 4 (the set contains itself)
Within the containing circle: Top left is a single circle, so it is 1. Top right is 2, so its a circle with another circle in it. Bottom left is three, so it contains both the previous symbols for 1 and a 2. And the final number is 4, so it has all the previous circle diagrams in it.
I think you were off by one? I think the single circle is more like zero, then the top right is 1, bottom left is 2, bottom right is 3, and the whole thing is 4.
Sometimes I think that after I die, I'm gonna confront whatever higher power type of consciousness that was in charge of this reality and I'm gonna ask "What the heck was the purpose of all that?"
And the answer is gonna be, "It was actually an off by one error" and I feel like it's gonna actually make sense at that point.
It could be defined that way. But your set is in a way more difficult to resolve as it has only one element. In the diagram the number of elements (4 sets) of the set is equal to the number 4 i.e. a set defines a number by simply counting its elements.
There are probably some other nice properties if you define it that way.
15 Comments
PrimeErective@startrek.website · 8 pts · 75d
Inscrutable, excellent
AppleTea@lemmy.zip · 14 pts · 75d
Each number is represented as a circle which contains the numbers below it.
4 contains 1 2 3 and 4 (the set contains itself)
Within the containing circle: Top left is a single circle, so it is 1. Top right is 2, so its a circle with another circle in it. Bottom left is three, so it contains both the previous symbols for 1 and a 2. And the final number is 4, so it has all the previous circle diagrams in it.
Lodespawn@aussie.zone · 10 pts · 75d
I may be missing something but why would 4 contain 4 when 3 doesn't contain 3 and 2 doesn't contain 2?
AppleTea@lemmy.zip · 19 pts · 75d
Excellent question, the answer is you've now reached the end of my understanding of set theory
agamemnonymous@sh.itjust.works · 13 pts · 75d
I think you were off by one? I think the single circle is more like zero, then the top right is 1, bottom left is 2, bottom right is 3, and the whole thing is 4.
topherclay@lemmy.world · 7 pts · 75d
Sometimes I think that after I die, I'm gonna confront whatever higher power type of consciousness that was in charge of this reality and I'm gonna ask "What the heck was the purpose of all that?"
And the answer is gonna be, "It was actually an off by one error" and I feel like it's gonna actually make sense at that point.
Lodespawn@aussie.zone · 5 pts · 75d
That would make sense because the fist circle is a null set with nothing in it
lemming741@lemmy.world · 6 pts · 75d
Lumidaub@feddit.org · 4 pts · 75d
Fedegenerate@fedinsfw.app · 3 pts · 75d
Now express -1/12 as a summation of null sets? It'd take a bit.
hayvan@piefed.world · 0 pts · 75d
Isn't four {{{{{}}}}}? The diagram shows more than that.
Redjard@reddthat.com · 3 pts · 75d
No, that's not how it's implemented in zfs. Probably to make implementing the basic arithmetic operations easier.
hayvan@piefed.world · 2 pts · 75d
TIL, thanks.
golgorath@lemmy.world · 2 pts · 75d
It could be defined that way. But your set is in a way more difficult to resolve as it has only one element. In the diagram the number of elements (4 sets) of the set is equal to the number 4 i.e. a set defines a number by simply counting its elements.
There are probably some other nice properties if you define it that way.
hayvan@piefed.world · 2 pts · 75d
Gotcha, thank you.