Mathematics: Quantity vs Quality

Something that the world of mathematics seems to have overlooked;
Absolute infinity cannot logically exist physically nor conceptually, “you can always add 1”.
For the exact same reason, absolute zero cannot exist physically nor conceptually… for qualities.

Absolute infinity is a conceptual impossibility.
Absolute zero is exactly equal to 1 / (absolute infinity) = an irrational concept.

One can have absolutely zero of a quantity. But one cannot have absolutely zero of a quality.

Potential, such as an electric potential, is a quality, not a quantity.

The reason that math runs across problems with infinite and infinitesimal concerns is that math is all about quantities, and only partially applicable to qualities (good for quantitative estimations).

Quantum physics is the ontology of a quantized reality and is a logically broken ontology, but that doesn’t mean that it isn’t useful for many kinds of quantitative estimations of reality. Classical physics was about qualitative reality, but at that time made the understandable error of including “rigid bodies”, quantitative entities. So Classical physics was a logically broken ontology also.

Rational Metaphysics: Affectance Ontology has no quantitative entities… no fixed quantities, including “absolute zero”. Even the things that I refer to as “points in space” can only logically exist as a changing of location, infinitesimal smears.

I might add that value is an issue of quality, not quantity.
And thus Value Ontology must remain quantitiless, else also be logically invalid, aka “broken ontology, BO”.

And perhaps a couple of illustrations will help;

In that pic, you can see that the distance from B to E is always going to be half of the distance from C to D. No matter how tall the triangle is, B-E must always be 1/2 of C-D.

But what happens when we gradually reduce the height of CD through absolute zero;

The entire time DC is being reduced, EB remains at exactly 1/2. But somehow, magically at exactly absolute zero the number suddenly changes for that single point. Either the distance EB instantly becomes exactly equal to DC or, defying logic, EB is only half of absolute zero. Either case is irrational.

In professional mathematics, the term “0/n” is undefined and the term “n/0” is indeterminate. Neither case makes rational sense.

So where does that leave the absolutely straight line concept? - Irrational, an oxymoron. It is an issue of ontology and the fact of it plays into Relativity, Uncertainty Principle, Quantum Physics, and Affectance.

You might want to, you know, read some mathematics before you claim that mathematicians overlook things. Actually infinite sets, as a concept, can always be added to to create a new set, also infinite.

That seems to be a strange claim, since physics is filled with things of zero charge. So it seems that the concept does just fine.

You may imagine this to be the case, but I know of no mathematics text that teaches this.

What about smooth analysis? What about calculi that deny the Archimedean principle? These systems seem to get along fine with infinitesimals.

Given that 0 = 0/2, where is the problem here? Different numbers have different mathematical properties than other numbers. Are you angry that 28 does not equal 8, but that 18 magically equals 8?

Not when n is a finite number and n does not equal 0. This is part of the definition of “/”. Please, look in an abstract algebra textbook.

That’s because it is not defined.

And you might want to, you know, actually think about what you are saying before you say it.
Or at least start working on how to do that.

Everything was fine when the Earth was flat with 4 corners as well.

Gee, maybe they overlooked something without informing you in print.
“But note that we are not looking at this…”

Given that something cannot be what it is and also be only half of what it is, there is a problem there.
A <> !A
…perhaps overlooked?

And exactly why would such a common occurrence remain undefined in the “perfect language”, the “language of God”?

And btw, “undefined” is not the same as “indeterminate”.

Most of the OP supports why absolute zero is impossible. But I’m not sure why you have concluded absolute infinity as irrational. So why is it irrational?

A square circle is an irrational concept because it can’t be constructed. Similarly absolute infinity cannot be mathematically constructed. There can be no rational mathematical expression for it other than to simply give it its own name.

“Absolute” means “nothing left out” or “none lacking” or “nothing more to add”.
If you have an infinite line, you have an infinite degree of points on that line, “infA”.
If you have two such lines, you have twice the degree of points, “2 * infA”.
If you have an infinite number of those lines, you have an infinite degree of infinite points, “infA * infA” or “infA^2”.
If you raise infA to the power of infA, you have “infA^infA” = “infB”.
If you raise infB to the power of infB, you have “infB^infB” = “infC”.
If you continue to raise every degree of infinity to its own value, you would have an infinite series of such values/degrees.
But then you can always just raise that series to its own value.
And raise an infinite number of such raised infinite series values to its new value.
And again, and again…

And you still won’t be expressing even one infinitesimal of absolute infinity.

Absolute zero is merely one over “absolute infinity”. And absolute infinity is merely one over “absolute zero”. If either is irrational, they are both irrational. Neither can be expressed other than to give them their own name, “absolute infinity” = “square circle” and “absolute zero” = “round square”.

Zeno knew this stuff wayyyyyy back in the day. The infinite divisibility stuff. Classic.

I agree with your definition.

I think so too.

I think I agree. 2 x infinity. Two infinities but not two absolute infinities, right?

Ok this is where I think your suggesting infinity times infinity. If so, I would argue that this = absolute infinity. (edited…forgot to mention it here but I do mention it later, that infinity times infinity or infinity to the power of infinity is either paradoxical or absolute infinity)

I think infinity to the power of infinity = absolute infinity.

I think multiplying absolute infinity by absolute infinity is either absolute infinity or paradoxical (Paradoxical because you can’t add anything to absolute infinity therefore you can’t multiply it by anything.)

I’m not sure if you can. How could you when nothing more can be added to absolute infinity? Absolute infinity encompasses and includes all infinities. The only time I think that absolute infinity multiplied by absolute infinity is not paradoxical, is like when you multiply 1 by 1 or put 1 to the power of 1. The outcome is always 1 as there is nothing more than one. Similarly with absolute infinity, the outcome is always absolute infinity as there is nothing more than absolute infinity.

I think that which is infinitely small or large must be the same thing. Infinity.

I would argue absolute zero is not and will never be because absolute infinity is and will always be. I don’t see how zero being over something could ever be possible. Say existence was finite. I don’t see how nothingness could just kick in. That’s why I think it has to be absolute infinity.

Why did you stop at “infinity raised to infinity”?

I realize that would at first seem an extraordinary height, but why not just square it?

Hey guys, I’m not trying to troll here. I don’t mean to make any point or take any side with this post. I sincerely hope that it doesn’t impact the thread negatively. However, if I don’t post this video right now, right here, I’ll feel weird about it. It’s too perfect.

[youtube]http://www.youtube.com/watch?v=cZh105_r2Qk[/youtube]

Infinity is the limit for infinitesimal minds.

I think I made a mistake. Initially I thought if something is finite in the x axis yet infinite in the y axis, then you can add to its x axis. But at the moment, I’m struggling with the idea of something being part finite yet part infinite thanks to your line example.

Your line example assumes the possibility of a hybrid finite/infinite thing and goes from there; but this only proves the impossibility of a “semi”-infinity. How does it disprove infinity or “absolute” infinity? I mean if absolute infinity and something like a hybrid infinity are two different things, then why should the impossibility of one conclude that the other is also impossible?

…just out of curiosity: Can you actually see my eyes crossing from where you are?

If you have two infinite things, does that constitute a “hybrid finite/infinite” thing?

Infinite merely means “endless”, “having no end”. Thus an infinite line has what we refer to as “an infinite number of points” which means “an endless number of points”.

But if you have two of such endless lines, you have twice as many points along any chosen section and thus twice as many as a whole. Both the single line and the double lines are endless, infinite, but one is “greater” than the other.

The question then becomes one of “Is there a limit to the greatness of the set of infinite lines?” If not, then you can have a endless, infinite, set of infinite lines. Or “infA^2 points”.

But then the question becomes whether you can have a limit to the greatness of that greatness of “infA^2”. And if not, then you can have “infA^3 points”.

But that series can never end. And that means that you can have “infA^infA points”.

But why stop there?

You can have an endless set of “infA^infA points” leading to “infA^infA^infA”.
And then “infA^infA^infA^infA”.

And even:
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And even with all of that, you STILL haven’t even gotten up to 1 infinitesimal of absolutely infinite.
Absolutely infinite, the highest possible order of the infinity, cannot be mathematically expressed except merely as its own name.

The terms “absolute” and “infinite” are mutually exclusive, a “square circle”, “oxymoron”.

You need a zero to make sense of negative numbers. If -n + n is not zero, then you have to throw out all arithmetic.
Real mathematicians figured this out long ago. Long before the ‘Quantum magi’ had anything to say about it.
James you are not fooling anyone with your "rational metaphysics’.Just give it up, take a nice holiday. No one but your sock puppets, are fooled by your nonsense. Even little children laugh at your bull.

It is impossible to have an actual “n” and a “-n”.

Mathematics presumes quantization, which only applies to mentally assigned identities, never reality.

Then You must be laughing pretty hard.
Children often laugh at their own fantasies, no matter what their age.

Until you can find anything actually wrong with it, I will take such comments as the egocentric jealousy that it is.
It is understandable that a cult would fear such a thing as RM.

James

I think I understood your example, which to be honest altered my view. But it did not alter my view regarding the possibility of absolute infinity, instead, it altered my view regarding the possibility of an infinity that is not absolute. I’m hoping to learn more on this as it would influence my other beliefs.

I’ve heard people say infinitely long, big, small or short but could these phrases mean anything other than infinity itself? I mean, on an infinite line the smallest measure and the largest measure, would either be infinity, or a smallest and largest measure would be impossible/undefined right? With this in mind I reached a similar conclusion regarding hybrid finite/infinite objects.

Considering the x y z axis, lets say there is an object that measures finite in terms of x and y but infinite in terms of z. I think it reasonable to call this object a hybrid because it is partly infinite (z axis) but also partly finite (x and y axis). I will now try to argue that all hybrid’s are impossible. This would then just leave absolute infinity as the only possibility.

If we try to mathematically work out the surface area or volume of any hybrid 3D object, we would have to multiply finite by infinity at some point. There are only two possible outcomes to this:

Outcome 1) Such a thing is absurd because you can never multiply something finite by something infinite. This logically implies that all hybrid objects are impossible.

Outcome 2) The answer will be infinity. This again implies that all hybrid objects are impossible. The area of a hybrid should not be infinity because it is part finite and this distinction must be clear in comparison to an infinite thing that is not part finite.

At the moment, the only thing I draw from this is that absolute infinity and absolute finiteness are both aspects of existence but a hybrid is not an aspect of existence. This would then mean an infinite line is impossible. This is why I don’t think your example disproves absolute infinity.

You say absolute infinity is impossible, what’s your position on an infinity that is not absolute?

You seem to be trying to use undergrad math on a graduate project. All infinities are not equal.

Two times “infinity”, in grad school, is not “infinity”, although it is “infinite”.
Infinite is a quality, not an amount/quantity. “Infinity” refers to an amount of the quality called “infinite”.

If we define as a particular size of infinity;
infA ≡ [1+1+1+ … +1]

Then we can use simple hyperreal mathematics to say that;
2 * infA = [2+2+2+2 … +2]

If you propose an object that has a length of infA (infinity), a width of 2, and depth of 2, then we can say that the volume of that object is;
Vol1 = infA * 2 * 2 = [4+4+4+ … +4]

And we can say that if you have two of those objects, the total volume occupied is;
Vol2 = 2 * Vol1 = [8+8+8+ … +8]

So our original length was infinite, our volume1 was infinite, and our volume2 was infinite, but none were equal to each other.

What that means is that the quantity of infinity can get bigger, thus it is NOT “absolute”.
“Absolute” means there is nothing that could make it any larger.

“Mathematics presumes quantization, which only applies to mentally assigned identities, never reality.”

Mathematics assumes no such thing.
’ Mentally assigned identities’?. You aren’t even trying, are you?

Do some math, not psychology. Then maybe people will take you seriously.

It seems that anyone who has any disagreement with your irrational metaphysics is in a cult. So the whole world is a cult and you are the only non member?

You are right about one thing, I am jealous of the fact that you can be wrong about so many things, and still think yourself a singular genius. It must be nice to be so alone. Carry on, my good man.

I define a “cult” member as anyone who absolutely insists on the collective thought even though they can’t even begin to defend it with any more than “they told me so and they can’t be wrong or they would tell me that they were wrong” or “Well you are a nobody and insane and a crackpot and liar and plagiarizer and just a general over all asshole”. And they almost always get irate at anyone challenging their scriptures.

If you or anyone else can find any ACTUAL logical flaw in anything I propose, I am happy to find out about it. But “logical flaw” doesn’t mean, “I don’t see the evidence”. It means, “Accepting consistent definitions, you have stated this and yet it contradicts what you stated about that”. And playing around with definitions in order to create a strawman issue doesn’t count either. Whatever definitions you or I use, must be maintained consistently through the reasoning.

I haven’t studied any maths beyond high school but I remember my philosophy lecturer from university showing something similar and I remember thinking to myself, what if they are both the same. I didn’t really pursue infinity much then but I am very interested in the concept now. I’l do some reading and hopefully reply within a week.

Thank you for the discussion.

Well, there are all kinds of proofs concerning the variation in size of different infinities.

But the bottom line is simply that one cannot say that he has added something to something else if that something else remains the same as it was. If the result is the same, then nothing was added, by definition.