Question: In mathematics &/or logic, what is the symbol between sets that are complementary and couldn’t exist without each other? Like parts of a homeostatic system of interlocking systems. And yes I mean irreducibly complex unity.
If this is a no-brainer, then just make fun of me and tell me the answer or where to look (I have at least 3 maybe 4 or 5 or more logic books I can consult). But please do not make something stupid up that you think I will believe because I am ignorant. I just have a bad memory about certain things.
I think you do it in reverse: you learn about the math, the logic, the ideas and the symbols that go with it, and THEN you consult that list if you want to use that symbol in a LATEX document. That document isn’t supposed to be a teaching tool, it’s just a list of symbols you can use in a piece of software.
Deletion may mean a lot of things, it’s a grab bag and in this case I thought secondly to let it go. Basically it was far into the future, kind of utopian and suspect to provisionally unsound assumptions, too rich with metaphor and wish thinking.
The inclusion of near term assumptions may have made more sense but could have been rejected because it was closer to a sound but iffy proposition.
But I shall watch myself and write less and deliberate it more before publishing it.
¿nature has a supernatural origin after which man is patterned, and so in actuality the supernatural & man are more nature than the co-created (super)nature—so the original pattern is more natural than even man???‽!!! YOU go add the extra shit to the beginning where there’s only one upside down?.
As you probably already know, I have a lot of trouble understanding a lot of what you say. In your opening post, for example, I have no idea what you mean when you talk about sets that “couldn’t exist without each other”. I also have no idea what “parts of a homeostatic system of interlocking systems” means.
As such, I can only guess and my best guess is that you’re looking for a “is the complement of” symbol. I am not personally aware of one; and when I go to a list of LaTeX symbols, I can’t find one.
Looks like set theory language is a pretty poor one.
What you can do instead is say something like “Let (A) and (B) be two sets. Let (A = B^\complement)”. That would tell us that (A) is the complement of (B). (B^\complement) stands for “the complement of B”. You can also say the same thing with (B’) and (\overline{B}). Ultimately, you can just say “(A) is the complement of (B)” but I don’t know what you’re trying to do.
There is a member of this forum called wtf. Despite his rather silly name, he’s a serious guy and he might be able to help you. He certainly knows more on the subject than I do. But as far as I can tell, he’s nowhere to be seen these days.
I’m afraid I can’t be of much help. Others have already noted that in set theory, if we have a set (X) and one of its subsets (A \subset X), we automatically have (A)'s complement relative to (X), denoted (A^c) or more accurately (X \setminus A), consisting of everything that’s an element of (X) that is not an element of (A).
But you have asked about “a homeostatic system of interlocking systems,” and you referred to irreducible complexity.
Those are more biological than mathematical. For example a person has a liver and a pancreas and a heart and skin and so forth, and it’s difficult to imagine any one of them existing without the others, at least in a living person.
Irreducible complexity I’ve only heard of in the context of intelligent design, a skeptical position on Darwinian evolution. The idea is that there are some biological systems that are vey complex, and that couldn’t have evolved from simpler systems because simpler systems couldn’t exist by themselves. The famous example is the bacterial flagellum, a little whip that bacteria move in order to propel themselves through liquids. The mechanism is an amazing little motor, very much in the design of a human-made rotary motor.
I recall there was a famous court case about the bacterial flagellum in which the intelligent design advocates won. [Edit – The ID folks lost].
None of this is spoken about by math. There’s no concept in math that says that “this system must exist if some other one does.” I imagine that mathematical biologists must have some terminology for this. Symbiosis perhaps, but your idea seems to be more than that.
You might see if you can find some mathematical biologists to answer this question. But it’s not a matter of pure math. In math if you can’t have A without B we’d just write “A implies B,” in other words it’s impossible for A to be true unless B is as well. But that relation usually applies to statements having logical relations to one another, not biological subsystems.
