Daniel

@who why didn't you answer the question? I answered your question. Fair is fair. If {} is disjoint from itself, {} ⊆ {} is true or false? If it's true then it cannot be disjoint from itself. If it's false it cannot be s subset of every set. Pick one! Is it true or false?

... deleted and stricken from the record, your honor

Please be honest. You're being stubborn. I think you "have an an idea of what it means" ~eye-rolls~ Let A = { 1 } Let B = { 1 , 2 , 3 } A ⊆ B = 1 A ∩ B = 1 1 ≠ {} Every element or group of elements can be represented as a set. The set is represtented as the element or elements enclosed in curly brackets. 1 = { 1 }. Better?

Disjunction is boolean "OR" isn't it? Edit: confirmed: https://en.m.wikipedia.org/wiki/Logical_disjunction I really think the best choice is "disjoint".

Let A = { 1 } Let B = { 1 , 2 , 3 } A ⊆ B = { 1 } A ∩ B = { 1 } { 1 } ≠ {} Any mistakes?

The intersection / union of a disjunction produces infinite negations, "mu" or "wu"... "無" It's the partnership of the disjointed sets which produces the action of nullification. From the wiki-monster: Causing to be non-existent. Original non-being. Those are both verbs. Actions. I'm bringing a mental construct ( many actually, infinitely many ) which systematically produces a realization of 無. That's the point.

How about this? If {} is disjoint from itself, {} ⊆ {} is true or false? If it's true then it cannot be disjoint from itself. If it's false it cannot be s subset of every set. Pick one! Is it true or false?

True! Shirt =/= not-shirt. Or Shirt is not (not-shirt). Distribute the "not". Shirt is shirt. Tautology. Identity.

Not true. I'm saying shoes aren't shirt. I said: "{ shoe } = { ... not-shirt, not-pants, not-glasses, not-hat, ... }"

Can't be, that's not disjointed is it? A ∩ A is not disjointed B ∩ B is not disjointed C ∩ C is not disjointed {} ∩ {} = {} is different from any other example of ∩. Similarly {} ⊆ A is different from any other example of ⊆. {} is "special". {} is unlike any other "set". It is "un-set". It inverts the meaning of any operator. It's the basis of "subraction".

Thank you!!! OK, ok... but, hopefully you know what I mean now? { 1 } = { ... not-0, not-2, not-3, not-4, not-5, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception. { shoe } = { ... not-shirt, not-pants, not-glasses, not-hat, ... } ad inifinitum for everything that wasn't, isn't, and won't with only 1 exception. You understand the notation now? The symbolism? The meaning of what I wrote? The nice thing about it being completely foreign to you, is, at least, one can see it is my own idea, not a copy from someone else. Even having minor flaws in how I speak/write about it ( example: { not-1 = "{ 1 } is false" } demonstrates this

I disgree. That's not the complete defintion of subset. A subset is A ∪ B = A *AND* A ∩ B = B. Both must be true. A ∪ {} = A But A ∩ {} =/= {}. It can't, by definition. {} is disjoint from all sets including itself. The solution is proper interpretation of {}. It flips the meaning, it inverts it. It ( {} ) is "contradicting", the action. That's it's actual meaning. {} is a subset of all sets is just a definition, not a derivation. Not a proof. Here, let me see if I can find it. It's just a mis-application of the law of non-contradiction. The logic is "If it cannot be proven that {} is NOT a subset, then it is assumed that it must be a subset." But that doesn't work for negative assertions: See here: https://plato.stanford.edu/entries/contradiction/. Search the page for "Socrates doesn't exist". Definition 1.3 Suppose A and B are sets. If every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is not true that every element of A is also an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B. Looking at the first sentence of the defintion given, If every element of A is also an element of B, then we say A is a subset of B. But this cannot be so because ∅ contains no elements! Thus it is not the case that ∅ ⊆ B, so it must be that ∅ ⊈ B. "Book of Proof, Third Edition, Richard Hammack" https://math.vcu.edu/directory/hammack.html See that? "So it must be..." That's applying the Truth table for implication, the weakest of the weak standards for truth. And, like I said, it's a defintion. A convention. An axiom. Convenient? Useful? Absolutley! True? Not really. It contradicts with the defintion of the empty-set, and empty-set, itself is contradictory. It's not a collection of elements. But once {} is interpretted properly, it all falls into place and plays nicely. But there's more than 1 set theory, ZFC is the easiest to learn, so that's what people learn, and assume it's the only one. They thinks it's law, like scriptural law, religious law. And let's me honest that's what axioms are. They're religious. Useful? Sure. But, if someone like me comes along... then the adherents to axiomatic set theory object vehemently :"Blasphemy! Burn him! He's a witch! Burn Him!" Set theory IS philosophy. All Math is philosophy. Anyway, did you check he credentials of the author from Duke University? PHD in Physics. Senior Lecturer. Many many journal articles.... https://scholars.duke.edu/person/rgb/publications

It's just an axiom, just a convention. A beloved convention, a useful tool. I think I saw it called a "convenient fiction".... Let me see if I can find something for you.... Found it! https://proofwiki.org/wiki/Definition:Empty_Set# 1965: J.A. Green: Sets and Groups: §1.3§1.3: If A,BA,B are disjoint, then A∩BA∩B is not really defined, because it has no elements. For this reason we introduce a conventional empty set, denoted ∅∅, to be thought of as a 'set with no elements'. Of course this is a set only by courtesy, but it is convenient to allow ∅∅ the status of a set. 2) 1968: Ian D. Macdonald: The Theory of Groups: Appendix: The best attitude towards the empty set ∅∅ is, perhaps, to regard it as an interesting curiosity, a convenient fiction. To say that x∈∅x∈∅ simply means that xx does not exist. Note that it is conveniently agreed that ∅∅ is a subset of every set, for elements of ∅∅ are supposed to possess every property. 3) 2000: James R. Munkres: Topology (2nd ed.): 11: Set Theory and Logic: §1§1: Fundamental Concepts Now some students are bothered with the notion of an "empty set". "How", they say, "can you have a set with nothing in it?" ... The empty set is only a convention, and mathematics could very well get along without it. But it is a very convenient convention, for it saves us a good deal of awkwardness in stating theorems This might also be useful. https://en.m.wikipedia.org/wiki/Empty_domain In first-order logic the empty domain is the empty set having no members. In traditional and classical logic domains are restrictedly non-empty in order that certain theorems be valid. Interpretations with an empty domain are shown to be a trivial case by a convention originating at least in 1927 with Bernays and Schönfinkel (though possibly earlier) but oft-attributed to Quine 1951.

I'm trying to think of a better way to describe it than the way I wrote it. If I consider 2 non-equal sets, A and B, like the picture I posted earlier, what is a real world example of A and B? My purpose is to better understand the concept of 'null' so, I'd like to slow down the "intersection" the "union", the action which produces "null" in my mind for the purpose of understanding the mechanics of it. ( in doing so, hopefully, ideally, a realization of Mu is produced , at least temporarily ) The easiest example, numerically, is A = { 1 } and B = { 2 }. But it could be any non-equal pairing. { A } and { B }, { dog } and { cat }, { swimming } and { walking }, { square } and { circle }, etc. If I intersect any of these pairs, what is produced? how can I imagine it? is it just an "empty box"? what does that mean, "empty-box"? { A } intersected with { B } = ????? it's not A, right? it's not B, right? it's not C either, right? D? nope E? nope F? nope 1? nope not 2 either not 3 not 4 not 5 not 6 what about negative numbers? nope. not -1 not -2 not -3 not -4 what about symbols? nope. not circle not square not star not rhombus what about actions? nope. not walking not sitting not standing not sleeping not dreaming what about ideas? love? nope hope? nope patience? nope { A } intersected with { B } isn't any of those! See what I mean? No matter what, nothing is included, and that nothingness is active. If I were to attempt to construct a set of { A } intersected with { B } in my mind, it would look like this: { ... not-A, not-B, not-C, not-D, not-E, not-F, ... , not-1, not-2, not-3, not-4, not-5, not-6, ... not-negative-1, not-negative-2, not-negative-3, not-negative-4, not-negative-5, not-negative-6, ... , not-circle, not-square, not-star, not-rhombus, ... , not-siting, not-standing, not-sleeping, not-dreaming, ... , not-love, not-hope, not-patience, ... } After typing this, maybe this is the easiest clarification of what I mean? { not-1 } = "{ 1 } is false"

I'm not getting is from anywhere. Hee-hee. ( I'm 'not' getting the 'not' from anywhere. which means the 'not' is coming from 'no-where'. ) Yes, I'm of russel's paradox, but, I don't see how it applies here, or invalidates what I wrote. Yes! If I recall, the point being made is the moniker "empty-set" is a misnomer. It's not a "set" it can't be. And the convention/axiom that the "empty-set" is a subet of all sets is actually false. But I'd need to re-read the document to be sure. Should I do that? I love this stuff, so I would be happy to do it if it's needed to correct my understanding, or, what I avoid a future mistake.

I believe.. confidently.. you are the pure-land. And I get to visit 'you' if I keep an open mind.

Brain-food? Soul-food? Both? A spiritual smoothie of glorious nothingness!

A lie is defined by the accuracy of the content? Yes or No?

why not here? six questions? five are yes/no? six answers would look like this: "yes, yes, yes, I don't know; I hadn't considered that, yes, yes" super simple.

{ 1, 2 , 3 } ∩ { 4 , 5 , 6 } = null = { ... not -5, not -4, not -3, not -2, not -1, not 0, not 1, not 2, not 3, not 4, not 5 ... } notice null includes "not 0" and it keeps going forever and nullifying. i haven't read this in a while, but i remember really liking it. it connects null, to the concept 'mu'. "Enlightenment is the realization of the null, the no-thing, Mu" https://webhome.phy.duke.edu/~rgb/Philosophy/axioms/axioms/Null_Set.html https://en.m.wikipedia.org/wiki/Mu_(negative)

I distiguish between 'zero' the number and 'null' the concept. when people speak about 'zero' philosophically, it seems that they are actually talking about 'null' not 'zero', but the two get conflated. 'zero' in my opinion is an object, 'null' is an action. 'null' is something that is happening. Also, when I consider infinity, it's +/- infinity ( ±∞ ). I include the negations (was, wasn't, is, isn't, will-be, won't, could-be).Technically, in mathematics, ∞ = ±∞. The ± is implied in the symbolism. This puts 0, if it were to be included in ∞ in the center, not at the extreme. It lives in the center of the number-line, doing nothing, contributing nothing, passive. Absolutley meaningless and without purpose. But! That is not what people are speaking about when 'zero', 'emptiness' 'nothingness' is discussed philosophically. The 'zero' that is being contemplated and considered is active. a resource, pool of nothingness, so to speak. like a great heavenly body of water, the 'firmament' for lack of better word. it's not a boring numeric 'zero' living in the middle of the number line. regarding being disconnected, I prefer the word disjointed, never coinciding. 'null' is the action of removal, like subtraction, like vaccuum. the operation, not the operator. it's energetic. Here's a diagram of how I envision 'null' which is often spoken of as 'zero', a source for manifestation. But I'm trying to illutrate that it's active. Energetic. The green arrows are "nullifying". It just keeps nullifying, forever and ever and always.

1) A lie is defined by the accuracy of the content? Yes or No? 2) Please respond to the example of the baseball game. Doesn't this demonstrate the remarkable accuracy of the simulation which is produced in the mind? Yes or No? 3) Please respond to the example of the toddler learning language. Doesn't this demonstrate the remarkable accuracy of the simulation which is produced in the mind? Yes or No? 4) Please respond to this example? If "color" did not exist how does anyone learn to drive a car? 5) Is this information below wrong? Isn't this an objective true and consistent defintion of 'color' Yes or No? 6) Didn't both of the links you brought provide this objective defintion? Yes or No? Cone cells, or cones, are photoreceptor cells in the retinas of vertebrates' eyes, including the human eye. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. https://en.m.wikipedia.org/wiki/Cone_cell

no not in grizzly country, not in alaska. just a lovely night, clear sky, the stars are out. quarter moon. quarter mile to home. I wonder what's just beyond my view? Can I hear anything other than my breath and the pads of my feet? what if this, what if that? heart is beating, I quicken my pace, and I'm home in seconds flat.

Of course, of course. Not talking about anything over the top. If I'm walking through the woods at night, and I have no doubt, is it exciting? Is it spooky? I don't see how it can be either. I know exactly what's going to happen.

Those are reasons.