# Thread: Is "1" proportional to Infinity?

1. Presented Argument:

1) "1" exists as "unity" and "wholeness".

2) As unity and wholeness "1" must maintain a self-reflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection
of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.

3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity.
In this respect all numbers are strictly structural extensions of 1.

4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and each other "1y" unto infinity. In this respect 1 reflects infinity.

5) All number, including "1", continually manifests through self-reflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.

6) The self-reflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes self-reflection as the "maintenance of structure through the maintenance of center(s)".

7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.

Agree, disagree, don't know? Explain why.

2. The answer to your question is simply: no. This is because the concepts of 1 and infinity are well defined in mathematics. No number can be proportional to infinity, because any division by infinity still leaves infinity.

Originally Posted by eodnhoj7
Presented Argument:

1) "1" exists as "unity" and "wholeness".
"Unity" and "wholeness" have nothing to do with the mathematical meaning of 1. Those words might have some weird metaphysical meaning to you, but they have nothing to do with mathematics.

1 can be defined using the concepts of set theory, or in various other ways. None of them involve "unity" or "wholeness".

As such, the remaining points of your post are irrelevant. (Which allows us to skip over the fact that they are meaningless word salad.)

BTW Posting this sort of drivel is the reason your posts get moved to Trash.

3. Originally Posted by Strange
The answer to your question is simply: no. This is because the concepts of 1 and infinity are well defined in mathematics. No number can be proportional to infinity, because any division by infinity still leaves infinity.

********Same with addition, subtraction, multiplication, exponentation and roots. I understand that. To summarized the above into one point:

All rational numbers are strictly a structural extension of 1 reflecting upon itself unto infinity.

The numbers exist in turn as structural extensions of infinity because b exists only because of a and c, c exists only because of b and d, so on and so forth. The infinite number of numbers is strictly an extension of both infinity as unity and 1 as a unified base.******

"Unity" and "wholeness" have nothing to do with the mathematical meaning of 1. Those words might have some weird metaphysical meaning to you, but they have nothing to do with mathematics.

1 can be defined using the concepts of set theory, or in various other ways. None of them involve "unity" or "wholeness".

As such, the remaining points of your post are irrelevant. (Which allows us to skip over the fact that they are meaningless word salad.)

BTW Posting this sort of drivel is the reason your posts get moved to Trash.
It's a legitimate question. I am not here to cause problems. It is strict mathematics. Physics cannot exist without math because it would be unable to define and of its properties. The ability for physics to define the physical universe exists partially because of quantitative reasoning allows a qualitative understanding.

Anyhow in regards to the 1 as "unity" problem you discussed. It is a legitimate point, however I do not think it is the full answer considering the following.

"One, sometimes referred to as unity,[2] is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number."

Skoog, Douglas. Principles of Instrumental Analysis. Brooks/Cole, 2007, p. 758.
https://en.wikipedia.org/wiki/1

(If you could post some reading material or quotes I would appreciate it).

"1" cannot sometimes be "unity" and sometimes "not be unity" otherwise "1" is strictly probabilistic and the foundations of modern mathematics would be found in "probability".

Even if one where to take "one" as a "unit" (and I am not arguing against that approach) how is a "unit" as a quality different from "unity" considering:

Unit is: "An individual, group, structure, or other entity regarded as an elementary structural or functional constituent of a whole."
https://www.thefreedictionary.com/unit

In this respect "1" as a "unity" is one as a "structure". All "structures" need a form of "symmetry" in order to exist. In this case it would be 1 reflecting upon itself.

That is another point where I am confused if you could help in that regards.

The problem, I am trying to understand within set theory, is that all sets in themselves are "1" and any set of numbers is a structural extension of that "1" set. This set is either part of a number of other sets, in order to gain stability or is in itself "1" set.

1) If it is the first answer then the set is a structural extension of infinite sets stemming from a "unity" as "infinity".
2) If it is the second answer then the set is "1" however exists if and only if the numbers manifesting the set are extensions of set as "1". These number in turn, through their existence form further sets, etc. unto infinity.

From a quantitative perspective the set must equal "1" otherwise "quality" is determining quantity. If a set is strictly a "qualitative" measurement then the number can be implied as "qualitative properties". If it is strictly quantitative, then the set itself is equal to "1".

That is a part of where my confusion stems from and there is more but I want to keep the post short.

4. Originally Posted by eodnhoj7
The problem, I am trying to understand within set theory, is that all sets in themselves are "1" and any set of numbers is a structural extension of that "1" set. This set is either part of a number of other sets, in order to gain stability or is in itself "1" set.
I don't know where you get the idea that "all sets are 1". That sounds pretty meaningless. (Surprise!)

It is possible to define numbers and their properties based purely on the axioms of set theory. In this case, the empty set is equivalent to zero. A set with 1 element is equivalent to "1", a set with 2 elements is equivalent to "2" and so on. Obviously, it is possible to define this without recourse to using numbers as I have here.

That is a part of where my confusion stems from and there is more but I want to keep the post short.
I guess your confusion comes about because you don't know what you are talking about. You probably need to study some basic mathematics and then move on to naive set theory. You will find them curiously devoid of your metaphysical mumbo-jumbo.

I know learning stuff can be hard work, but it is much more rewarding in the long run than just making crap up. And, as a bonus, you will be able to get a bit more respect on science forums.

p.s. yeah, "unity" can be used as a synonym for 1. Big deal.

5. I don't know where you get the idea that "all sets are 1". That sounds pretty meaningless. (Surprise!)

It is possible to define numbers and their properties based purely on the axioms of set theory. In this case, the empty set is equivalent to zero. A set with 1 element is equivalent to "1", a set with 2 elements is equivalent to "2" and so on. Obviously, it is possible to define this with recourse to suing numbers as I have here.

*** That is my point exactly I think we hit some common ground:

1) "A" set with 1 element is equivalent to "1". It is still "A" or "1" set.

2) "A" set with 2 elements is equivalent to "2". It is still "A" or "1" set. In this respect this set would be equal to both (1,2) at the same time in different respects. I am not arguing about the set equaling "2". It is in the response that we equate "A" set to a seperate non-equal number such as 2 only when 2 is also a structural extension of one.

There is no contradition of two answer occuring at the same time in different respects.

********

I guess your confusion comes about because you don't know what you are talking about. You probably need to study some basic mathematics and then move on to naive set theory. You will find them curiously devoid of your metaphysical mumbo-jumbo.

*****I claimed confusion from the beginning. There is no disagreement.

I know learning stuff can be hard work, but it is much more rewarding in the long run than just making crap up. And, as a bonus, you will be able to get a bit more respect on science forums.

*****Asking questions through the form of an argument or hypothesis is the spirit of the scientific method.

p.s. yeah, "unity" can be used as a synonym for 1. Big deal.

*****
"a word or phrase that means exactly or nearly the same as another word or phrase in the same language, for example shut is a synonym of close."
https://www.bing.com/search?q=synony...020185D2E8BCD6

Besides I argued that one is proportional to infinity. How is this a problem considering is shows a "linkage".

6. Originally Posted by eodnhoj7
Besides I argued that one is proportional to infinity. How is this a problem considering is shows a "linkage".
1 is obviously not proportional to infinity. Proportion means that some division operation is possible. This obviously is not the case with infinity.

As you seem to be unable/unwilling to understand that, the thread seems pointless.

*** That is my point exactly I think we hit some common ground:
But I was pointing out that you were talking nonsense...

*****Asking questions through the form of an argument or hypothesis is the spirit of the scientific method.
It would be more productive to ask questions based on a basic education in the subject. Starting from a position of total ignorance and asking questions about things you have made up is not so productive.

7. My laptop freezes with the quote button, I don't like it either. I have to empty some files. To get on point:

Infinity is not defined when any arithmatic function applied to it is a equivalent to "no definable".

Infinity is not a number we can perform any mathematical operations on without equating it to "ever approaching zero" or no definition. 1/∞ exists as a fractal only, as far as I understand.

What does Infinity Divided by Infinity Equal? « Phil for Humanity

That is the problem I am trying to observe as many of these numbers exist if and only if there is infinity as they must continually "reflect" (or manifested through arithmatic tables) in order to exist as "stabile".

So unless I am reading something wrong...you are wrong. They argue "undefined", not infinity. The problem I have is that if infinity is undefined when an arithmatic function is applied to it, it must be stable as
it contains all number. Quantitative (numerical) infinity is equivalent to all number ∀1n = ∞. All number cannot be added to all number as all number already exists; that is also undefinable.

1) The problem is "infinity" implies existence as number exists if and only if they manifest unto infinity. 1n cannot exist unless their are infinitely further numbers to quantify it as 1n.
2) "1" implies existence as number exists if and only if they are structural extensions of 1.
3) 1 and quantitative infinity seem to cycle between eachother as neither can exist without the other as all rational numbers are merely reflections of "1" unto infinity. 1 exists if and only if their is quantitative
infinity. Quantitative Infinity exists if and only if their is one. In this respect they can be observed as dualistic: ⟨1|∞⟩.

4) Infinity must contain "1" as an element otherwise it would not exist. 1 must contain infinity as an element otherwise it would not exist.
5) All number contains as an element "1" and "1" exists through self-reflection if and only if there is infinity as it must reflect itself through infinite number to infinitely exist. If One does not contain as an
element "infinity" is is not "stable" as it is "finite". If Infinity does not contain 1 as an element neither is it stable as it does not contain "all".

6) Because 1 as a unit or "unity" must both contain as an element and be an element of infinity as: 1 ∋ ∞ and 1 ∈ ∞ which would be similiar but not equal to ∞/1 and 1/∞ as "fractions". This is considering if x contains
as an element y, the element y can be observed as a degree of x.

∞/1 and 1/∞ can be observed as "proportional to eachother" as fractions even though these fractions in themselves cannot equate to anything other than themselves.

so ∞/1 ∝ 1/∞

The problem occurs as "lack of definition" is proportional to "lack of definition" cannot exist as thier is no definition to be proportional too.

7) In this respect ∞/1 ∝ 1/∞ cannot exist except as 1nx/1ny and 1ny/1nx as both contains as elements and are elements of 1nx and 1ny. 1nx/1ny and 1ny/1nx are striclty observation of "division" in one respect and "ratios"
in another for a ratio exists if an only if their is division and vice versa.

In this respect 1 and ∞ contain as an element and are an element of "proportionality/ratios" and "division". In this respect, and possiblity this respect only, 1 is proportional to infinity as they both contain
as an element and are an element of 1nx and 1ny.

or (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)}

Assuming the equation is correct, and that is where I need an opinion, One is proportional to infinity maybe only in this respect.

8. Again, you are posting nonsense based on your total ignorance. You seem to think that because you know absolutely nothing then no one else does either.

Infinity is very well defined as a mathematical entity. That is how we know that the answer to your question is obviously "no".

Or, as you keep posting nonsense: "no, of course not you blithering idiot"

Your carefully enumerated points are just gibberish. All they do is demonstrate that you don't have a clue what you are talking about.

For example, this random collection of mathematical symbols: (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)} is just meaningless. You have obviously seen these symbols somewhere and thought "if I put some of these together in my post it will make me look intelligent". It doesn't it make you look like a fool.

Both your words and your "equations" look like a cat walked over the keyboard.

Please go an learn some basic mathematics before posting more of this nonsense.

9. Originally Posted by eodnhoj7
My laptop freezes with the quote button, I don't like it either.
When you click the quote button, and see the little spinning icon, click on the spinning icon again, and then the quote function works. This is a workaround.

Is "1" proportional to infinity?

You are in the mathematics forum, so you must use the well established mathematical meanings for terms like "1", "proportional" and "infinity"

Using proper mathematics, 1 is most definitely NOT proportional to infinity.

Stop making stuff up. Learn mathematics. End of story. End of thread. Thread closed.

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