Simplified:

ℝ is the set of INFINITE, continuous, unbounded numeric phenomena.

We’re using non-numeric, axiomatic token INFINITE to describe the primary distinguishing property of set REAL.

INFINITE is the adjective form of INFINITY.

Tokens INFINITY and REAL and REAL’s noun-form REALITY are therefore synonymous.

INFINITY is a set.

QED. Huzzah!

(This is what needs the comment)

 

Lol. Yeah, that post was out there in TheoryLand and certainly not "too terribly obvious (speaking of)." I was actually more talking about the theoretics in this previous post, which is more ultimately model-bound in my estimation:

I didn't understand that, either, but I'll try again.

The reason we don’t know what the REAL numbers are is because the token REAL is a component of superset token REALITY. One can’t scientifically show partiality to using congenital token REAL and dismiss token REALITY. REAL is that which is part of the set REALITY. We use token REAL as the base token to describe “what is.” It’s either REAL or it’s fake and/or non-existent.

This paragraph is very difficult to parse. Does "REAL" in "REAL numbers" refer to REALITY or to ℝ?

The reals are INFINITE and IRRATIONAL, as is the set of them called INFINITY, which could also be called REALITY.

The set of real numbers is called ℝ; why confuse things be using a new label, particularly an overloaded label such as "INFINITY"?

Each and every number in ℝ is finite. The cardinality of ℝ as a set is uncountable. Though most numbers in ℝ are irrational, an infinite amount of them are rational. For example, the number 42 is a real number.

To fractionate ℕ infinitely is to create ℝ.

If by "fractionate" you mean divide, then fractionating ℕ gives us the rationals ℚ. Note that ℕ and ℚ have the same countable cardinality; they are sets of equal size, much smaller than ℝ.

The quantity 1 can be fractionated by n as n -> ∞ and its fractions in turn transpose into set ℝ.

Not quite. Consider the sequence \( \{a_n\} \), defined by \[ a_n = \frac{1}{n} \qquad \forall n \in \mathbb{N} \] Letting \( n \to \infty \), we get the sequence \[ \{ a_n \} = \{ 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \cdots , 0 \} \] Clearly, this is a proper subset of ℚ, and so a proper subset of ℝ, and so no where near a construction of ℝ.

INFINITY is the asymptotic boundary of ℝ, and is the basis of REAL geometry, or indivisible geometric form that is the reference point for knowing what is.

A few paragraphs above, you said that INFINITY is a set, another name for ℝ. So, how can INFINITY also be "the asymptotic boundary of ℝ"?

I take "REAL geometry" to mean Euclidean geometry, i.e., a Hilbert space over the field of real numbers. But this is incompatible with your notion of "indivisible geometric form". Anything that includes ℝ is going to be infinitely divisible, as ℝ is a continuum. Any segment from a line, no matter how small you make it, will have an uncountable amount of points.

The simplest machine which can take infinite ℝ inputs is f(x)=mx, and it spatializes itself as the most elementary INFINITE geometric OBJECT (line).

In order for the machinery of f(x)=mx to rationally input and output any of ℝ, it too must hail from REALITY or INFINITY as an actual object to do so.

No idea what you're trying to say here.

Since INFINITY is defined as not a number but an extra-numeric set of numbers, the mathematical machinery must too be an extra-numeric object to accommodate it.

I take "mathematical machinery" to mean "function", and I agree that functions are non-numeric objects. They are maps between sets.

The machinery is a MIND-based infinite object that is the basis of infinite geometric 5D form.

This is jibberish to me.

 

I appreciate this response, because it entirely illustrates again (for the 900th time) why we have to start from scratch to insure 100% parity of semantic approach (yours being an established, academically sound, peer-reviewed, white-paper ready one, and mine is akin to a murder hornet's that just escaped from the same lab that created COVID).

I want to see "a map of the cat," if you catch my drift. I'm Kronecker 2.0 here coming from the place that number sets are #jobsecurity in disguise (e.g., <a href> vs <FRIGGINWEBLINK>, and "prior to sets of numbers were created" there were "fingers" and "macaroons."

There's NUMBERS and INFINITY to me.

There's a relationship between them. What's their true relationship?

42 is FINITE — MAYBE — but why?

What if "42" is itself an innately stored wave "token" that stands for "a unique infinite set of continuous elements that happen to be labeled 42 vs 43?"

That's the kind of department I'm coming from. But that's not recognized by science (understandably, and respectfully up to who knows, maybe this discussion), nor has it been delineated within its semantic framework. That's why we burn the house down and start from scratch, because obviously the 46 unlabeled dials on the oscilloscope (the "congenital semantics") might have something to do with understanding the full amount of information it affords about the circuit.

 

I understand the dilemma — and perhaps we can set these off somehow — but for internal conceptual use, SENSE is specifically used obviously and liberally and never SENSOR, so I feel like not defining SENSE as part of the mental BIOS might be problematic (and please feel free to suggest a word for this — Congenital Semantic Architecture? Innate Human Lexical Framework? Native Linguistic Schema? Something to denote the nativity of these terms).

What's wrong with LOGIC or LOGICAL for a word that captures the internal "makes conceptual sense" meaning? I offered a few other candidates, as well.

Here's a hash-out of the terms I think need attention first, and perhaps one will inform the other — and yes, I do believe we can define these terms with very essential scientifically sound essences and emancipate them permanently from Nebuland

Pick a couple of the most fundamental and define them.

When one closes one's eyes, and clears it entirely, one can make a base observation upon the intended state of his own mind. The most basic, obvious phrase one can utter is:

IN MY MIND, I SEE NOTHING.​

​

Ugh, that is not obvious to me at all. In fact, I disagree with its premise. Assuming that we know what we mean by "IN MY MIND" (hah!), when I close my eyes I most definitely see something. My optical system doesn't stop working just because my somewhat opaque eyelids have covered my photosensors. I see changing colors and shapes and patterns. A simple experiment easily demonstrates that we are indeed still seeing -- point a bright flashlight near your closed eyes and turn it on. Try it.

"SEE" in this case is an internal sense, because one can extrapolate this phrase to all 4 remaining senses: "I touch/taste/smell/hear NOTHING in my mind." NOTHING is defined in terms of SOMETHING as the potential state of SOMETHING.

In most situations, the seeing my closed eyes are doing is external (proven by the flashlight experiment). There are ways to drastically reduce external stimuli, such as sensory deprivation chambers, and even in those cases the (external) senses are still working. People in such chambers report strong hallucinations after a while, as it seems that the brain -- in its struggle to latch on to whatever sensory input is available -- amplifies and augments the data with its own.

I can, however, get on board with the SOMETHING/NOTHING dichotomy. To wit,

SOMETHING is the CONCEPT developed by associating the detection of an external stimulus as a distinct STATE.

For example, as you're walking through the woods, the auditory system is responding to various sounds -- birds chirping, wind blowing through the trees -- that the brain deems unimportant. Each of these acoustic events is processed but not given a distinct state. Suddenly, you hear the loud crack of a branch breaking nearby. Your brain deems this acoustic event important and gives it a distinct state; you heard something, possibly indicating a threat.

As this detection process goes on essentially constantly in our lives, with all of our senses, we develop an association of such distinct perceptual events that is abstracted from the particular details of any single event. This absract association is the CONCEPT of SOMETHING, The SOMETHING stands for any particular sound we hear, movement we see, etc. It is the distinction itself. And from SOMETHING, it's a short conceptual step to recognize NOTHING, i.e., the absence of SOMETHING.

After one SENSES what's THERE, one can now utter this phrase:

I KNOW SOMETHING IS THERE.​

I'd say that "I BELIEVE SOMETHING IS THERE" is more accurate. I take KNOW to imply something infallible; I KNOW that 2 + 2 = 4.

To KNOW SOMETHING IS THERE is to declare a FACT to one's self concerning its EXISTENCE in the mind.

But that is a BELIEF of existence, and doesn't speak to any ontological truth. A person having a psychotic episode may strongly believe that Abraham Lincoln is attacking him with a machete, but we wouldn't say that Abe has existence. Hopefully you will agree that "exists to me" is not a sufficient property of EXISTENCE.

 

What about "the dress?" . . . . I do believe the photo represents the actual dress, but is disseminating different waves out somehow from that one photo of it. It's NOT the people viewing it.

"Disseminating different waves out" is crazy talk. One lovely afternoon, I sat at a table with my extended family and I showed everyone the image on my phone. The phone was passed from person to person, each proclaiming their interpretation of the dress's colors, and each completely incredulous that anyone could disagree. We each saw the same image from the same device in the same lighting conditions. Then, as if we had intuited that perhaps the phone was playing a trick on us, we huddled around the phone and looked at the image at the same time. If the electromagnetic wavelengths eminating from the phone were changing depending on who was holding it, we would have all seen what the person who was holding it saw. But the colors did not change for any of us -- we all still saw the same colors we had originally and incompatibly seen.

The only reasonable conclusion is that human perception is truly subjective, and the colors in The Dress image just happen to be an edge case that came to the forefront. We likely experience countless perceptual differences every day that simply don't come up in conversation.

 

ℝ is the set of INFINITE, continuous, unbounded numeric phenomena.

False. ℝ is the set of real numbers. Specifically, ℝ is the unique (up to isomorphisms) ordered field for which every subset has a least-upper bound. Every element in ℝ is finite.

These are indisputable properties of ℝ, so I don't know what you're describing.

We’re using non-numeric, axiomatic token INFINITE to describe the primary distinguishing property of set REAL.

As I defined it, INFINITE is not an axiom. More so, INFINITE applies to COUNTING, and so is related to ℕ, not ℝ. The set ℝ is uncountable.

INFINITE is the adjective form of INFINITY.

Tokens INFINITY and REAL and REAL’s noun-form REALITY are therefore synonymous.

INFINITY is a set.

QED. Huzzah!

LOL at your attempt to prove that INFINITY and REALITY are synonymous based on grammatical function -- they're both nouns, therefore they're the same thing!

 

KNOW that 2 + 2 = 4.

Hmm maybe let's see..

 

"Disseminating different waves out" is crazy talk. One lovely afternoon, I sat at a table with my extended family and I showed everyone the image on my phone. The phone was passed from person to person, each proclaiming their interpretation of the dress's colors, and each completely incredulous that anyone could disagree. We each saw the same image from the same device in the same lighting conditions. Then, as if we had intuited that perhaps the phone was playing a trick on us, we huddled around the phone and looked at the image at the same time. If the electromagnetic wavelengths eminating from the phone were changing depending on who was holding it, we would have all seen what the person who was holding it saw. But the colors did not change for any of us -- we all still saw the same colors we had originally and incompatibly seen.

The only reasonable conclusion is that human perception is truly subjective, and the colors in The Dress image just happen to be an edge case that came to the forefront. We likely experience countless perceptual differences every day that simply don't come up in conversation.

Crazy-talk?!? This is coming from a guy who thinks his family members are voltage states until proven otherwise!

LOL! ;--)

Several decades ago, if I told you the information in a particle is affecting another particle miles away, you'd say THAT TOO is crazy talk! Or that there is something that exists like qubits.

What do you think QED is about? As someone looks at the particle, it shifts as a partial function of the observer looking at it!!!

If the woman walked in as she did on Ellen's TV set into your family room, NOT ONE person would say the dress was not black and midnight blue.

We are NOT talking about "shades" of colors, or "the girl spinning to the left or right.' This is WHITE as DARK BLUE, and BLACK as GOLD.

So edge-case I think not. When's the last time GREEN and RED traffic lights were confused by 7 BILLION PEOPLE again?

 

42 is FINITE — MAYBE — but why?

Because when we count to 42, we eventually stop. Halting/stopping is a sufficient condition for what it means to be finite.

What about Pi, which has "infinite" decimal digits? Well, Pi is not a counting number, so we can't count to Pi. But Pi is assuredly finite. How do we know? Well, Pi is part of an ordered field (ℝ), and this gives us another sufficient condition for being finite: A number \( x \) is finite if it is less than a finite number \( a \). We know that 4, which is a counting number, is finite. And we know that \( \pi < 4 \). Therefore, Pi is finite. QED.

What if "42" is itself an innately stored wave "token" that stands for "a unique infinite set of continuous elements that happen to be labeled 42 vs 43?"

What if "42" is part of an alien recipe for chicken soup?

The thing that makes the number represented by "42" a number is that it has a unique set of numeric properties. The label doesn't matter, only the properties. This is so important it bears repeating in bold: a number's label has no significance, only its properties.

When we write the symbols "42", we are referring to a particular number with a unique set of properties. These properties -- e.g., "the unique composite number with prime factors 2, 3, and 7" -- are necessary. You're entirely free to say that "42" stands for the way a cow's legs shiver on moonless nights, but that has nothing to do with the number 42 as it doesn't share the necessary properties.

So, unless your "unique infinite set of continuous elements" has exactly the same properties as the number 42, you're describing something entirely different.

 

Hmm maybe let's see..

View attachment 206348

I'm assuming you realize why the steps above are invalid and were just trying to be funny. But if you actually believe it to be a valid proof, consider what "a - b" means when "a = b".

 

False. ℝ is the set of real numbers. Specifically, ℝ is the unique (up to isomorphisms) ordered field for which every subset has a least-upper bound. Every element in ℝ is finite.

These are indisputable properties of ℝ, so I don't know what you're describing.

Every element of ℝ is essentially either an integer, rational, or irrational number... they're all describing infinite, continuous phenomena essentially, that's why we invoke ℝ for continuum mathematics.

As I defined it, INFINITE is not an axiom. More so, INFINITE applies to COUNTING, and so is related to ℕ, not ℝ. The set ℝ is uncountable.

You said INFINITY is an axiom early on!! 100% in writing in earlier posts. You said, paraphrased, that's "how we deal with it when we're using it to compute" — we make it an axiom. And I said that was "fairy dust", and we went through the whole conversation that n+1 is not working, because infinity is NOT a number. It is an AXIOM. Therefore, INFINITE is the adjective form of that INFINITY AXIOM, and its properties can be used an extension of that form!

LOL at your attempt to prove that INFINITY and REALITY are synonymous based on grammatical function -- they're both nouns, therefore they're the same thing!

I have an amped up version of the graphic for you here:



"Based on grammatical function???" Based on CORE MEANING (oh that's right, we haven't defined "MEANING"). We use "REAL" as an ADJECTIVE. Adjectives are derivations of the set NOUNS. There is no adjective without NOUNS. AXIOMS are nouns. Axiomatic is an adjective to describe a sentence that is an AXIOM.

I have ZERO understanding why you think that's not legit, for the sake of an infinite Pete.

 

Crazy-talk?!? This is coming from a guy who thinks his family members are voltage states until proven otherwise!

Well, at least my form of crazy talk is plausible.

Several decades ago, if I told you the information in a particle is affecting another particle miles away, you'd say THAT TOO is crazy talk! Or that there is something that exists like qubits.

If you used a time machine to give Isaac Newton a couple of late 20th century graduate physics text books (and a couple of undergrad math textbooks to get him up to speed), he'd probably really want to do some experiments for himself, but I have no doubt he'd be convinced of the plausibility of quantum entanglement. Why? Because the text books build up the theory step-wise with logical and physical arguments. You can't read it, understand it, and just go nah.

Now, tell Newton that we have 5D souls that interface INFINITY with the REAL numbers and indivisible geometry. He'd probably ignore you and try not to make eye contact with the crazy lady.

What do you think QED is about? As someone looks at the particle, it shifts as a partial function of the observer looking at it!!!

Huh? Are you talking about QED as in quantum electrodynamics? That's not what QED is about. There are neither particles nor observers in QED.

We are NOT talking about "shades" of colors, or "the girl spinning to the left or right.' This is WHITE as DARK BLUE, and BLACK as GOLD.

So edge-case I think not. When's the last time GREEN and RED traffic lights were confused by 7 BILLION PEOPLE again?

Well, actually, green and red are particularly troublesome for a large subset of people with colorblindness. But to your main point, you agree that WHITE can be easily changed to DARK BLUE with a filter, yes? So, if the simple act of moving a piece of glass in front of our eyes can so drastically change colors, what's so surprising that our extremely complicated optical systems are not all tuned the same? In which case, wouldn't we expect certain stimuli to straddle the fuzzy lines of perception tuning?

Consider that, though most humans are trichromatic -- we have three types of color-sensitive photoreceptors -- some humans are actually tetrachromatic. Such people see more color than we do. If such extreme physiological perception differences are possible, why would you have a hard time believing that subtle perception differences are the norm?

 

Because when we count to 42, we eventually stop. Halting/stopping is a sufficient condition for what it means to be finite.

And who says it's finite and not infinite at the same time? Like INFINITY we use as an axiom that is defined outside of numbers but ALSO bound it to make a number!

You were the guy who keeps saying numbers are not connected, and that 0111010 is not a number. Who is to say "42" is the "countable digit" after 41? Who's to say they're related?

What about Pi, which has "infinite" decimal digits? Well, Pi is not a counting number, so we can't count to Pi. But Pi is assuredly finite. How do we know? Well, Pi is part of an ordered field (ℝ), and this gives us another sufficient condition for being finite: A number \( x \) is finite if it is less than a finite number \( a \). We know that 4, which is a counting number, is finite. And we know that \( \pi < 4 \). Therefore, Pi is finite. QED.

Says the guy who just said we can map every ℝ-based n to between 0 and 1??? That is no proof pi is a finite number. We're still counting. You think it's finite at the 900 quadrillionth digit? It hails from the relationship between the circumference and diameter which need to be defined INTERNALLY and built from scratch using the real infinite numbers, not in the FINITE world we live in that is bounding everything and their mother into discrete elements.

What if "42" is part of an alien recipe for chicken soup?

The thing that makes the number represented by "42" a number is that it has a unique set of numeric properties. The label doesn't matter, only the properties. This is so important it bears repeating in bold: a number's label has no significance, only its properties.

Exactly. I'm saying it IS part of an alien recipe for chicken soup. It is a LABEL for some unique infinity. You can't say we can make the infinite n to between 0 and 1 and not say it's weird we don't understand between the relationship of infinity and the numeric!

When we write the symbols "42", we are referring to a particular number with a unique set of properties. These properties -- e.g., "the unique composite number with prime factors 2, 3, and 7" -- are necessary. You're entirely free to say that "42" stands for the way a cow's legs shiver on moonless nights, but that has nothing to do with the number 42 as it doesn't share the necessary properties.

And I'd like to burn that house down right now, because you only have base 2, two fingers to work with, and numbers are like 0101011011011100 and 10100110 and 1101010. And now tell me what is related to what. Computers have no problem dealing with numbers having no "properties."

So, unless your "unique infinite set of continuous elements" has exactly the same properties as the number 42, you're describing something entirely different.

That's correct. They all have the same properties. Ask a computer that's able to compute with them (and yes, 0's and 1's are base 2 numbers). They are all labels for unique infinities. The properties are a post-facto organization invention.

 

Every element of ℝ is essentially either an integer, rational, or irrational number... they're all describing infinite, continuous phenomena essentially, that's why we invoke ℝ for continuum mathematics.

Huh? What infinite, continuous phenomenon does the number 3 describe?

I think we need to agree that we can't invent new definitions for established things, especially not highly technical things like mathematical objects. If you want to specifically invoke ℝ, you must accept what ℝ is as it is defined by mathematicians. It took them literally thousands of years to figure out how to describe ℝ, and we shouldn't assume that we could do better in 15 minutes.

If you want something with properties beyond that which ℝ has, you should create a new symbol for it and describe exactly what it is. But ℝ is ℝ.

You said INFINITY is an axiom early on!! 100% in writing in earlier posts. You said, paraphrased, that's "how we deal with it when we're using it to compute" — we make it an axiom. And I said that was "fairy dust", and we went through the whole conversation that n+1 is not working, because infinity is NOT a number. It is an AXIOM. Therefore, INFINITE is the adjective form of that INFINITY AXIOM, and its properties can be used an extension of that form!

Sigh. Look here:
https://forum.allaboutcircuits.com/threads/information-in-analog-wave.168244/post-1505104

I literally say, "INFINITY is a CONCEPT, not an AXIOM" and go on to describe how it is derived using the "n +1" CONCEPT. You are mistaking what I said about infinity (note no caps) in historical context. In most mathematical fields, infinity is treated as an axiom. I mentioned that early on in our discussion; it wasn't part of our model building. (I don't even think we had started building our model yet.)

I have an amped up version of the graphic for you here:

ROFL, love it!

"Based on grammatical function???" Based on CORE MEANING (oh that's right, we haven't defined "MEANING"). We use "REAL" as an ADJECTIVE. Adjectives are derivations of the set NOUNS. There is no adjective without NOUNS. AXIOMS are nouns. Axiomatic is an adjective to describe a sentence that is an AXIOM.

I have ZERO understanding why you think that's not legit, for the sake of an infinite Pete.

As I understood it, you were trying to show that INFINITY and REALITY are synonymous because they're both nouns, which is of course absurd. I still don't get what nouns and adjectives have to do with any of this.

 

Can you edit #613? Looks like you missed a /QUOTE tag.

 

Well, at least my form of crazy talk is plausible.

Quick experiment: Go tell all of your family members they exist only as logic states. Then ask them which which one of us, based on that conclusion, should drive the other to loony bin. Report back here.

If you used a time machine to give Isaac Newton a couple of late 20th century graduate physics text books (and a couple of undergrad math textbooks to get him up to speed), he'd probably really want to do some experiments for himself, but I have no doubt he'd be convinced of the plausibility of quantum entanglement. Why? Because the text books build up the theory step-wise with logical and physical arguments. You can't read it, understand it, and just go nah.

EINSTEIN had a problem with these concepts, man! "Does the moon only exist when you're looking at it?"

As you argued earlier, there is NOTHING INTUITIVE about the universe we are in. My explanation for that dress is actually MORE inline with recent awarenesses that we are essentially in a deterministic hologram! It's HELLA plausible!

Now, tell Newton that we have 5D souls that interface INFINITY with the REAL numbers and indivisible geometry. He'd probably ignore you and try not to make eye contact with the crazy lady.

Hahaha! He'd not only agree with me, he'd DEBKAC the hell out of that statement by turning to DANIEL 9 and write 1.2 million words on a chronological preterist account of how Christ is returning as the triumphant one over the Catholic antichrist, only after he mixed 3 concocted potions together in his alchemy lab while balancing a prism on his naked chest, and hanging from the ceiling upside down to see if he could prove why CHRONOS can be called Saturn in the Magha constellation of Sidereal Leo and if there's anything to his thoughts that Israel returning as a nation will mark the end of time as a function of its 70 weeks prophecy, and how the 62 and 7 elements must be kept discrete as separate accounts of first and second coming because they're doing "violence to the language of Daniel" to combine them as other theologians did at the time. He wrote more on that than natural science — FACTS. Then he'd INSIST you had a soul and spirit, and INSIST that only GOD directs gravity and chastise anyone else who thought otherwise, while writing Principia. MORE FACTS. He was more theological metaphysicist than physicist.

Huh? Are you talking about QED as in quantum electrodynamics? That's not what QED is about. There are neither particles nor observers in QED.

Oh whatever the F on the label. Lol. That big debate with Einstein and everyone else. He couldn't stand the whole nonlocation, entanglement issue. Invoked "Does the moon only exist when you look at it?"

Well, actually, green and red are particularly troublesome for a large subset of people with colorblindness. But to your main point, you agree that WHITE can be easily changed to DARK BLUE with a filter, yes? So, if the simple act of moving a piece of glass in front of our eyes can so drastically change colors, what's so surprising that our extremely complicated optical systems are not all tuned the same? In which case, wouldn't we expect certain stimuli to straddle the fuzzy lines of perception tuning?

We'll discuss this in the car trip to the ward. ;--) No, there are slight anomalies only. We have built a traffic system that 99% of humanity that can easily use between green, yellow, and red in every light condition. Anyone who thinks otherwise will have a hard time arguing his subjective stance to the cop who pulled him over and judge that tickets him.

Consider that, though most humans are trichromatic -- we have three types of color-sensitive photoreceptors -- some humans are actually tetrachromatic. Such people see more color than we do. If such extreme physiological perception differences are possible, why would you have a hard time believing that subtle perception differences are the norm?

There has NEVER been something that utterly grotesque in disparity. Never, ever, ever in the history of chromatic science or human life, period. It's a nuclear bomb to a every other scud missile. This is echoed by every true expert that has looked at it. We are NOT talking about a business-as-usual disparity, or anything that can be compared to any other study of any kind at any time anywhere, except for its audio equivalent in "Laurel vs. Yanny."

 

Can you edit #613? Looks like you missed a /QUOTE tag.

Yep, sorry (the top /QUOTE was missing and made the whole thing a quote).

 

Huh? What infinite, continuous phenomenon does the number 3 describe?

I think we need to agree that we can't invent new definitions for established things, especially not highly technical things like mathematical objects. If you want to specifically invoke ℝ, you must accept what ℝ is as it is defined by mathematicians. It took them literally thousands of years to figure out how to describe ℝ, and we shouldn't assume that we could do better in 15 minutes.

If you want something with properties beyond that which ℝ has, you should create a new symbol for it and describe exactly what it is. But ℝ is ℝ.


Sigh. Look here:
https://forum.allaboutcircuits.com/threads/information-in-analog-wave.168244/post-1505104

I literally say, "INFINITY is a CONCEPT, not an AXIOM" and go on to describe how it is derived using the "n +1" CONCEPT. You are mistaking what I said about infinity (note no caps) in historical context. In most mathematical fields, infinity is treated as an axiom. I mentioned that early on in our discussion; it wasn't part of our model building. (I don't even think we had started building our model yet.)

FFS, OK. I've got bare-essence awarenesses I know that are innately true using base semantics and are HOSED by their co-locative semantics in science's existing definitions!

As I understood it, you were trying to show that INFINITY and REALITY are synonymous because they're both nouns, which is of course absurd. I still don't get what nouns and adjectives have to do with any of this.

No. LOL! I'm showing the synonymity of their MEANING by co-opting their adjective form from their noun essence.
This stuff is ALL SEMANTICALLY CLUSTERED, and it's the reason we have to get at the BIOS to pull apart what all of it means at bare essence levels!

A repeating number is INFINITE. Why can you use INFINITE? Because you know what INFINITY is. INFINITE is the adjective form of the noun essence which allows you to describe it as such.

Assume for a moment "REAL" is the set of all irrational numbers (humor that for a moment). They never terminate, they are unbounded, and they are all connected, like all the numbers between 0 and 1.

INFINITY is the word we use to describe unboundedness outside of any kind of continuum of numbers. INFINITE is its adjective form.

The set of REAL would then be INFINITE, as tied to definition of INFINITY.

REAL also is an adjective, it has no meaning unless you define it first in terms of its NOUN essence. What is its noun essence? REALITY.
Something completely f*cking undefined by science, but is the utter FOUNDATION of everything we are talking about!

Stop laughing, you!

INFINITY and REAL are tied at the BIOS zero-and-one-foot-pedals level! And that's the "WEIRD" thing you're commenting on before from a 4GL lens!!

 

Huh? What infinite, continuous phenomenon does the number 3 describe?

Let's say 3 is just a label for a "UNIQUE" infinity-as-thing. Instantiate a theoretical cube of continuous points in your mind, each line containing infinite points. Label it 1. Then do another cube next to it. Label it 2. Then another cube. Label it 3. How does "3" relate to the geometry of the cube and its infinite points? Could 3 mean "this unique group of infinite points?"

I think we need to agree that we can't invent new definitions for established things, especially not highly technical things like mathematical objects.

Yes, I agree — though this is problematic(!) Because "REAL" is a token in the BIOS and is being used by something that may indeed not fully encapsulate it properly!

 

As you argued earlier, there is NOTHING INTUITIVE about the universe we are in. My explanation for that dress is actually MORE inline with recent awarenesses that we are essentially in a deterministic hologram! It's HELLA plausible!

Negative, Houston. Your explanation, unlike quantum mechanics, has no foundation. Even if we are a deterministic hologram, we are a deterministic hologram that obeys the laws of quantum mechanics. It is necessarily so. Any theory that's more accurate than quantum mechanics will nonetheless have quantum mechanics within it. Bell's inequalities are indisputable and must ultimately be accounted for by any theory, including your 5D hologram.

Hahaha! He'd not only agree with me, he'd DEBKAC the hell out of that statement by turning to DANIEL 9 and write 1.2 million words on a chronological preterist account of how Christ is returning as the triumphant one over the Catholic antichrist, only after he mixed 3 concocted potions together in his alchemy lab while balancing a prism on his naked chest, and hanging from the ceiling upside down to see if he could prove why CHRONOS can be called Saturn in the Magha constellation of Sidereal Leo and if there's anything to his thoughts that Israel returning as a nation will mark the end of time as a function of its 70 weeks prophecy, and how the 62 and 7 elements must be kept discrete as separate accounts of first and second coming because they're doing "violence to the language of Daniel" to combine them as other theologians did at the time. He wrote more on that than natural science — FACTS. Then he'd INSIST you had a soul and spirit, and INSIST that only GOD directs gravity and chastise anyone else who thought otherwise, while writing Principia. MORE FACTS. He was more theological metaphysicist than physicist.

LOL, true, Newton was a mystical sunofabitch. Nevertheless, he well knew the difference between a good and a bad mathematical argument when he saw one. Note that numerology isn't wrong in the same way that saying "2 + 2 = 5" is wrong. Numerology is really just finding patterns where there are none, which is entirely different than making logical contradictions.

Oh whatever the F on the label. Lol. That big debate with Einstein and everyone else. He couldn't stand the whole nonlocation, entanglement issue. Invoked "Does the moon only exist when you look at it?"

Einstein personally hated what quantum mechanics implies, but he never called it wrong -- he couldn't! What he did say was that quantum mechanics is incomplete, which it obviously is. But observers have nothing to do with it.

We'll discuss this in the car trip to the ward. ;--) No, there are slight anomalies only. We have built a traffic system that 99% of humanity that can easily use between green, yellow, and red in every light condition. Anyone who thinks otherwise will have a hard time arguing his subjective stance to the cop who pulled him over and judge that tickets him.

My high school friend Scott was color blind. We'd drive around in his car together and, if it was late at night and there wasn't any traffic on the road, he'd ask me what color the traffic lights where. Without other cars to infer the stop/go condition, he had no idea what color the lights were. I highly doubt he's physiologically unique.

There has NEVER been something that utterly grotesque in disparity. Never, ever, ever in the history of chromatic science or human life, period. It's a nuclear bomb to a every other scud missile. This is echoed by every expert that has looked at it. We are NOT talking about a business-as-usual disparity, or anything that can be compared to any other study of any kind at any time anywhere, except for its audio equivalent in "Laurel vs. Yanny."

Erm, how would you know? Perception is, by its nature, personal and so any discrepancies are unlikely to be noticed except by dumb luck. People don't usually walk around describing their perceptions.

You claim that The Dress is uniquely grotesque, except for Laurel vs Yanny (so not actually unique). But Laurel vs Yanny is not unique, either; there's, for instance, Brainstorm vs Green Needle. The fact that there's an entire catalogue of visual/audio illusions and curiosities speaks to the very fuzziness of perception. The McGurk effect is a profoundly grotesque example of how data from our senses mix in forming perceptions. The Dress is just one example of perceptual ambiguity, and you're claiming it as the unique glitch in the matrix that reveals the 5D infrastructure. I'll take Occam's razor for $200, Alex.