Basic set theory disproves omni-states

You can either count one or two separately or at the same time … But it is a different experience to do them in these different ways such that it’s un reconcilable …

If you count 1 by itself, you can’t know what it’s like to count 1 and 2 at the same time, and vice versa…

This is not only a knowledge issue, it is a presence and potence issue as well!

That which is possible for any one being is proven to be impossible for any one being!

I see no set theory, basic or otherwise, in your post. Perhaps you can clarify which principles of set theory you think you are referencing.

The set of all sets cannot be a subset!!!

I’m actually angry at you at this point, because I’ve solved some very serious number theory, and you called me an idiot… For all I know, you’re stealing it from me and getting a doctorate, it’s like I have to walk you through as a child and you still call me an idiot!

I am one of 2 people ever born who sequenced the rational numbers (not reals) uniquely.

I am the only person who proved that cantors diagonal argument is not a disproof.

And I proved that every sequence is counted by an algorithm shorter than it!

And you still treat me like the worst crap of shit ever born!!

Oh, and I’m the sole discoverer of dimensional flooding !!

That’s untrue. I have never been disrespectful to you. I have always treated you with the utmost respect and civility as I corrected your mathematical misunderstandings. Perhaps you have me confused with someone else.

If you can reference a single word I’ve ever written on this forum that is insulting to you, as opposed to being merely a correction of your mathematics, then I will apologize. Failing that, perhaps you can understand that you are mistaken about my having ever called you a name or made any disparaging personal remark about you at all.

My comments to you have been strictly mathematical.

I categorically deny ever having been disrespectful to you in any way. I have spent a fair amount of time trying to explain to you your mathematical errors, of which there are many. I have always been respectful and tried my best to work with you mathematically.

If you mean that by simply disagreeing with your math I would be disrespectful and insulting, that’s one thing. But if you can tell the difference between disagreeing with you and being disrespectful to you, then I’m sure after you review my posts you’ll agree that I’ve always been respectful.

Here is my entire posting history on this forum. I’m sure after you read it you’ll realize you have me confused with someone else.

Once you realize that, we can get back to talking about set theory.

search.php?author_id=42558&sr=posts

Ok… Well let it go because you have been polite!

You said I hadn’t counted the rational numbers (which I did) and accused me of saying I counted the reals (which you corrected me on before) when I used dimensional flooding to say I can’t (although I’m still trying to figure it out btw).

The set of all sets cannot be a subset! That’s basic number theory ! Set theory !

The set of all sets which are and are not members of themselves is considered the ultimate set… The set of all sets !

The confusion comes in the same value but it’s really not the same value because of heirarchy…

The set of all sets always has a different hierarchy, it is a distinct entity, and is only cursorily related to its subset (set) in kind, but not in value …

Set of all set (the word set appears twice) but they have different hierarchy and are thus of differing value!

There is no paradox here!

The set of all sets is never a subset, ever, ever, ever…

Even if it seems to contain itself, it’s not the same value!!

There is no such thing as the set if all sets that contains itself!

The set of all sets never contains itself as a subset …

What’s important to understand here is that if you draw a 1 on top of a 2 artistically, it is totally different than 1 or 2 by themselves… All three are mutually exclusive and don’t allow for a set of all sets because of this mutual exclusivity …

A one drawn on top of a two is a different entity and 1 or 2

And 2 is different than 1…

There is no such thing as the set that contains itself…

A square divided into 4 squares, is a square, but it is a square divided into 4 squares and not JUST a square!!!

If you use infinity to divide each square into 4 squares to create a set within a set, it either cannot be done because it’s a super function , or if completed, no longer becomes 4 squares, but a solid filled in square…

Thus there are no longer 4 squares in the superset square or any of it’s subsets!!!

The point!!!

The set of all sets is never a subset!

I wanted to articulate this point…

If a tesselation of lizards making a giant lizard is a set within itself… Then why is one larger than the other???

Order of magnitude MUST be considered !!!

Oh, and the rationals cannot be well ordered!!

You have to use a scatter technique to order them!!

The interpolation of wholes and fractionals requires that it not be well ordered… Otherwise you run into dimensional flooding !!

I’m still trying to solve the interpolation of reals to this day!!

Holy shit!!!

I figured out how to count the reals !!!

You need to use subtraction to do it!!!

Holy shit!!!

You have to subtract the expanding dimensional flooding at the end!!

Wow!!

Wow!!

It’s 3 dimensional !!!

Wow!

I’m checking my work wtf…

Basically, you can’t construct the reals from a growing finite list… You need an initial infinite list…

Which is the second dimension of the list of rationals, THEN you use the list of rationals in combinatorics with ITSELF !!!

I’m still checking the proof…

Citation needed. Seems to me the set of all sets would be a subset of the set of all mathematical concepts, the set of all non-physical things, the set of all infinite sets, and probably a bunch of others.

If this is basic number theory, please provide a citation saying it is so.

There is no set of all sets, that’s a consequence of Russell’s paradox. en.wikipedia.org/wiki/Russell%27s_paradox.

The collection of all sets in standard set theory is a proper class; that is, it’s a collection that’s “too big” to be a set.

The “set of all nonphysical things” is not well-defined, but it’s worth noting that all mathematical sets contain only nonphysical things. In math we only consider pure sets; that is, sets whose members are also sets. We start with the empty set and build up all the other sets out of that. There is no “set of books” or “set of apples” for example. Those may be considered to be sets in grade school, but they are not sets in mathematics.

The “set of all mathematical concepts” is not well-defined and doesn’t make any sense in this context. Nor is there a set of all infinite sets, for exactly the same reason that there’s no set of all sets.

Emmm… that isn’t how set theory works.

Russel’s “paradox” is merely a simple mind game, a trick to the simple minded eye. But the issue is that he spoke specifically of “the set of sets that are not a member of themselves”. The trick is that such a category is incoherent/nonsensical/oxymoronic. It is exactly the same as saying “this statement is false”. The category and statement appear at first glance to be reasonable concepts. But in fact they are “square circles”, or “oxymorons”.

That isn’t how mathematics works either.

That is exactly how set theory works. The meaning of Russell’s paradox in the context of the historical development of early set theory is well known and it’s not what you say it is.

Russell’s paradox is a technical demonstration that shows that the principle of unrestricted set formation leads to a logical contradiction. The remedy is to simply disallow unrestricted set formatation, either via type theory (Russell’s idea) or the Axiom of Separation (Zermelo’s idea, which has become standard).

In the early days of set theory, say from Cantor’s paper of 1874 through the early 1900’s, the idea of a set was vague. Today we call the set theory of this era naive set theory, in contrast with the formal set theory that developed from that time to the present.

In those early days, a set was thought of as the collection of things in the universe that made some predicate true. A predicate is a statement that is either true or false when you plug in some individual. For example “T(x)” might mean the statement that “x is tall.” In that form it has no truth value. It does acquire a truth value if you plug in a specific individual for x. For example T(Lebron James) is true and T(Tom Thumb) is false.

Unrestricted set formation is the principle that you can form a set out of the things that make some predicate true. The set of tall people, the set of books, the set of even numbers.

However Russell came along and showed that unrestricted set formation leads to a logical contradiction. Specifically if you consider the predicate “x ∉ x” then the resulting set both does and doesn’t contain itself. That’s a contradiction. Therefore we must reject unrestricted set formation.

The fix was suggested by Ernst Zermelo. He said that you could only form a set from an already existing set. To form a set you must first have some other set. Then you can cut that set down by a predicate to form a new one.

For example if N is the set of natural numbers {0, 1, 2, 3, …} and we form the set of all elements of N that are not members of themselves, we get the natural numbers. After all 1 is not a member of itself, nor is 2, etc. There is no contradiction!

Zermelo formalized his idea as the Axom of Specification. That axiom (actually an axiom schema) says that if you have a set S, and a predicate P, then you can form the set of all elements s in S such that P(s). No more contradiction. Starting with an existing set makes the contradiction go away. And as a corollary, there is no set of all sets; because if there were we’d just apply Russell’s predicate to it and generate the same contradiction.

That’s all Russell’s paradox is. It’s a proof that unrestricted set formation (also called unrestricted comprehension) leads to a contradiction. Zermelo supplied the patch, and life goes on. (It’s also worth noting that type theory is experiencing renewed interest these days, due to the influence of computer science and some other things).

As a separate but related topic, it turns out that the only reason a set can’t be a member of itself is that we assume an axiom that says so, namely the axiom of regularity.

If instead we assume the negation of regularity we get a system of set theory in which some sets can be members of themselves. Such a system is called a non well-founded set theory. Non well-founded set theories are an obscure topic of study today, but you never know when a mathematical idea will turn out to be useful. Well-founded set theories are perfectly consistent from a logical point of view; and logically consistent but intuitively “wrong” ideas often turn out to be important. Consider non-Euclidean geometry, or for that matter negative numbers, which were once thought to be impossible.

How so?

Oh and ps – Of course there are square circles. The unit circle is a square in the taxicab metric. There’s a picture of a square circle on the linked page.

That is exactly what I said that it was. It is a specific type of set definition which contradicts itself, exactly like the statement “This statement is false”.

And “unrestricted set formation” is like saying “unrestricted sentence formation”. Of course there are rules to maintain coherence in forming useful and meaningful statements and categories (“sets”). What kind of idiot doesn’t realize that? Anyone can form incoherent sentences. So what?

Mathematics is logic applied to quantities. It is not concerned with “quantity of what?”, just as logic is not concerned with the truth-to-reality of the premises of an argument (“equation” or “syllogism”). Math does not proclaim that there is no referenced ontological substance or items, merely that it doesn’t bother with whether there is or not because the relationship between the quantities is independent of what is being counted or measured.

So yes, “all apples” is a “set” or a “quantity” in mathematics even though math didn’t care if it was apples or anything else.

To me, it is obvious that Minkowski had mental issues, but regardless, he enjoyed playing with notions of diverse ontological construct without concern of rationality. That is why he tripped out over Einstein’s revelation concerning the speed of light and encouraged Special Relativity, which turned out to be fallacious. I suspect without the influence of Minkowski, Einstein would not have tried to create an independent ontology, “Relativity Theory”, but would have instead properly incorporated his thoughts into what we now call Classical Physics.

As one of Minkowski’s mental trips, he tried to imagine the universe made of discrete squares of reality. And in that kind of ontology, every length would have to be a series of 90 degree turns, like traveling through city blocks (hence “Taxicab Geometry”). And in such an ontology a circle, being a geometry with equal radius at all points, cannot exist. The closest thing to it would be a square. But even Minkowski’s square (called a “circle”) does not have equal radius at all points, not even close. Instead, it has equal distances at specific points/corners, while leaving out the distance and points between those corners because they do not follow the desired result. Minkowski was always willing to forgo reality in order to proclaim innovation (his catharsis).

And besides any of that, the term “square-circle” is in reference specifically to a euclidean geometry. One cannot alter the ontology in the midst of an argument in order to justify one’s desired conclusion.

The set of all sets includes your entire post.

QED

2op

True, but if you count all sets at once [like the universe does]?

The sets are not the same, no, and their different features are indeed not reconcilable.

Do you mean that e.g. if Gods perfection was the set of one/s, it cannot also be for the set of twos, as they wouldn’t be perfection if that had already been attributed to ones [the set of]?

But what if God uses all maths and patterns and in the third party ~ y’know like nature does? Perfection would then be a balance of forces which yields a world, or multiple worlds/realms = creation {as an on-going event matrix}. or in other words, there is no mathematical perfection, but something else instead!?

One cannot count the real numbers simply because there are more real numbers than there are whole numbers with which to count them.