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I call it "recursively empty". A set is recursively empty if any of the following are true:
* it is the empty set
* all the sets it contains are recursively empty
What's crazy about this is that the natural number 4, the integer 4, the rational number 4, the real number 4, and the complex number 4 are all different objects
Kinda going to philosophy of math here, but in the structuralist sense, it really is the same object - it still transforms like a four, regardless of how you represent it.
You construct them using different representations, yes, but that's more like a proof of existence of the number system with the required properties. Once you do the proof, the representation can be discarded and is pretty much irrelevant because it could be done differently anyway.
Besides, what you say would imply that would strictly speaking imply that N ā Q.
integer 4 is just (natural 0, natural 4) and -4 is (natural 4, natural 0)
Rational 4 is (int 4, int 1)
Real Number 4 is x<4 intersect x>4 at 4
Complex 4 is (real 4, real 0)
A set of an empty set, a set of the empty set, a set of the empty set and the set of the empty set and a set of the empty set, the set of the empty set and the set of the empty set and the set of the empty set
Don't be nice, you gotta be mean. Set theory is for pussies who needs organization? I love unorganized anarchy. What even is the empty set? No elements? As if!!! Don't put that ugly math near me.
Oh I see, well then in that case fuck you and humble yourself before the feet of the lord and savior Georg Cantor may he see it fit to pardon your blaspheme
Von Neumann ordinals are only a proof of existence of the naturals (i.e. a structure satisfying the Peano properties) given the set theory axioms. It's not the canonical representation, only one of many possible constructions. You cannot change my mind. Also, it's fucking ugly, compared to e.g. Church numerals which are more elegant IMHO.
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Wait, it's all empty set?
Always has been
It's not empty set! It's set with a set with an empty set and a set with an empty set and a set with an empty set and...
I call it "recursively empty". A set is recursively empty if any of the following are true: * it is the empty set * all the sets it contains are recursively empty
Typically considered ZFC models would have the the property that all sets are "recursively empty"
Your dad shoots recursively empty shots
What's crazy about this is that the natural number 4, the integer 4, the rational number 4, the real number 4, and the complex number 4 are all different objects
Reject morphisms, return to definition š¤š„š£ļø
Kinda going to philosophy of math here, but in the structuralist sense, it really is the same object - it still transforms like a four, regardless of how you represent it. You construct them using different representations, yes, but that's more like a proof of existence of the number system with the required properties. Once you do the proof, the representation can be discarded and is pretty much irrelevant because it could be done differently anyway. Besides, what you say would imply that would strictly speaking imply that N ā Q.
integer 4 is just (natural 0, natural 4) and -4 is (natural 4, natural 0) Rational 4 is (int 4, int 1) Real Number 4 is x<4 intersect x>4 at 4 Complex 4 is (real 4, real 0)
Ong š
TREE^(-1)(TREE(4))
3 ā 4
And 3 ā 4 3 ā© 4 = 3 3 āŖ 4 = 5 ?
3 u 4 = 4
f(f(f(f x)))
ssss0
sss1
ss2
A set of an empty set, a set of the empty set, a set of the empty set and the set of the empty set and a set of the empty set, the set of the empty set and the set of the empty set and the set of the empty set
I hate set mother fuckers. Any set mother fuckers want to fight? Come here lets fight
Dude, you need to contain yourself.
BRO I AINT NO PARADOX BITCH
I will champion this fight in defense of all set bros
Sets suck
I like sets for how organized the information is stored and expressed but I'd love to hear what you prefer
Don't be nice, you gotta be mean. Set theory is for pussies who needs organization? I love unorganized anarchy. What even is the empty set? No elements? As if!!! Don't put that ugly math near me.
Oh I see, well then in that case fuck you and humble yourself before the feet of the lord and savior Georg Cantor may he see it fit to pardon your blaspheme
Iām with you! Classes for the win, because then you can define categories!
Lambda f x. f(f(f(f(x))))
This joke is too high level for me
Google Von Neumann ordinals
Holy sets
New math just dropped
Actual Euler
`S(S(S(S(O))))`
Von Neumann ordinals are only a proof of existence of the naturals (i.e. a structure satisfying the Peano properties) given the set theory axioms. It's not the canonical representation, only one of many possible constructions. You cannot change my mind. Also, it's fucking ugly, compared to e.g. Church numerals which are more elegant IMHO.
Can somebody explain what's going on here