/sci/ - Science & Math

>>11771271
0 and emptiness is a double edged sword, yes now computation becomes easier for human minds, but I think the ancients didn't include it for a reason, because nature doesn't consider or compute empty sets. I have recently concluded 0 to be a mathematical crutch and it takes math away from describing the domain of nature to an abstract domain of thought

>>11771271
Why is the empty set clearly not existing? You cant prove or disprove the empty set exists. That's why it's a postulate. The reason we assert it exists is because you need to assume something exists in order to have any objects in math. The empty set is the only candidate. Also, if you take two disjoint sets, what is their intersection then? Suddenly set operations are awful to deal with. I guess we have no sets anyway so it doesn't matter.

>>11771316
>if you take two disjoint sets, what is their intersection then?
they have no intersection, because they are disjoint

>>11771289
I don't get why people throw their arms up about 0. What is so mystical about it? Why would "the ancients" have any better insight than modern humans?

>>11771325
I'd rather do math where I dont have to worry about whether or not my sets coincide

>>11771316
>what is what platonists actually believe
lmao

>>11771271
Wtf are you talking about ? If this is what you have problems with, you might as well cut your losses and give up on math altogether.
How is an empty set so unfathomable of a concept ? Have you never had an empty bag or an empty bookshelf ?

>>11771340
What are you objecting to? I just told you the reason mathematicians use the ZFC axioms as they are. It is apparent you've put no real thought to your position whatsoever

>>11771339
in reality you already worry about whether or not things coincide, so you are already ontologically committed to anon's account of disjunction unless you are willing to say that it doesn't exist. your mathematical weirdness is only added on top of that.

>>11771271
The empty set is not an element of A, retard, its a subset of A.
The empty set is a subset of any set.

>>11771348
i'm laughing at your total inability to interact with a lay person's worries about the weirdness in your account of mathematical objects. also>>11771356

>>11771347
>empty bag doesn't contain anything
true
>empty bag contains nothing
false, there is no such thing as nothing

>another infinite set thread

>>11771364
also i must go to sleep now it's almost 10pm so lets forget about this whole issue good night m8

>>11771336
0 deserves no hate, its a great tool and line of reasoning, and opens up lines of reasoning like limits approaching 0. But to your question on its mysticism. Its the same reason why the olmec's possessed a more precise measure of the solar year than what Western civilization was to achieve until the 1800's. Maps from antiquity possess accurate longitude, which again, we didn't have until the 1700's. We clook at the geometry of various works of ancient art, the pyramids, mega structures. Engineered and ordaned at a level of precision not reproducable again until the industrial revolution, all why communication the geometry of the earth.

Its easy, in light of archaeology, to treat the description of numbers of the ancients very seriously, obviously they knew of 0, its properties, its potential, but in the works they imbued to communicate with us through the aeons, it is neglected.

My hypothesis portends that the knowledge the ancients would pass on wouldn't be some arbitrary number system or vector field like the minkowski space or the anti-desitter space, or even the field of irrational numbers. The ancients desired to communicate with us a specific vector field, mathematical field of space, that of nature.

bump

>>11771357
this

>>11771390
noo, it's a "the empty set doesn't exist" thread, its toooootally different

>>11771364
>>11771356
Alright man

>>11771356
What? The empty set doesn't exist or not exist. You assume it exists, along with the rest of the ZFC axioms. The rest of math follows. You can go ahead and assume it doesn't exist, that is fine. You can even use philosophical reasons to justify one way or the other, but that bas nothing to do with math. But you must know, without the empty set, theres no mathematics. Without it there are no mathematical objects

>>11775137
You do not actually need an axiom which says that there exists an empty set: It follows from the Axiom of Infinity.

>>11775153
ITT: let's assume infinite objects exist to prove that the empty set exists.

>>11775215
You are a very silly person.
The Axiom of Infinity says that there exists a set with certain properties, one of which is that it contains the empty set as an element. Any other properties of said set are irrelevant for deducing that it contains the empty set, by its definition.

>>11775234
ZF axiomatics is batshit crazy. Dually to some retards who happen to be concerned about the size of their peepee large cardinals, the incels that cherry-picked the list of axioms aimed for the lower number of them without any care for their legibility. You could perfectly choose another bigger set of axioms that clearly separates the theory of hereditarily finite sets from BLACKED ordinals.

>>11775265
So you do not like or understand mathematics. Are you Norman?

>>11775265
You could stick to Peano Arithmetic if you like to restrict yourself in that way. Lots of people do research in PA. This theory is pretty much the same as ZF with AI replaced by its negation. And it has infinitely many axioms, which suits your quest for having more axioms.

>>11775283
The absolute degenerative state of /sci/.

I am willing to bet I know more formal deduction systems and their meta-theoretical properties than any faggot posting in this thread.

>>11771388
>>>/x/

>>11775428
Thank you for letting us know about the elevated state of your wisdom.