Infinitely bigger, infinitesimal, and bigger infinity size

[Fixxed]

Basically this thread is to discuss about how infinities work

What the different between perceiving something as infinitesimal and be infinitely larger than something??? I think it just same

Because infinitesimal it self it mean divided something infinitely, something that close to 0 but not 0. Like 1/∞ and 0.999... . Less than any real number. It mean infinitesimal is "something" that being smaller and smaller to infinity, if we want to have that "something" again from the infinitesimall "thing" we must revers it or enlarge it again and again to infinity, mean being infinitely larger than the "thing". So being infinitely larger than something is already perceive them as infinitesimal

So what about bigger infinity???
Basically it mean bigger size of infinity, is mean if something is infinity then it is more infinity than that

I think infinitely bigger and infinitesimal is not equal to bigger infinity. Because bigger infinity have some infinity that can be compare to it size, when the two is we can give finite size to compare with their size

So are we use infinitely larger = infinitesimal < bigger infinity
Or
All the three is equal. Infinitely larger = infinitesimal = bigger infinity

 

[Iamunanimousinthat]

Perceiving something as infinitesimal does not make something infinitesimal. Take two objects, A and B. If A is infinite in size, and B is finite in size, I have seen people say things like, "B is infinitesimal to A". That's not true. B is not infinitesimal and will never be infinitesimal no matter how big A is. Finite and infinite things can never be infinitesimal. Sure you may be be able to get away, "perceives as" but that's just hyperbole, subjective, or a metaphor and not reality.

And someone can correct me if I am wrong, but this site uses Cantor's set theory and Aleph numbers. Infinitesimals are not apart of that system. So it really confuses me that people are using infinitesimals in conjunction with set theory and aleph numbers, and bigger infinities.

There is a number system, the hyperreal system that incorporates infinitesimals and infinites. But these infinites are different from the infinites in set theory and aleph numbers and cannot be used as a one to one exchange. For example in the hyper reals, ω represents infinity. And you can 2ω and ω+1, and ω^2 and so and so on, and those are all distinct values of infinity, and someone can correct me if I am wrong, can have bigger or smaller values than each other.

But to answer your questions:

Infinitesimals are not equal to any infinity. They are smaller than any finite positive number including any real positive number. Your example of 0.999 is not an example of an infinitesimal.

"Infinitely larger" depends on what you are comparing. Any infinite value is infinitely larger than any finite value. I am not sure if finite values are infinitely larger than infinitesimal values, but someone else can answer to that.

"Bigger infinity" depends again on the type of math you are talking. In set theory, what this site uses, Aleph-0 represents a countable set of infinite things. A bigger infinity would Aleph-1 which represents an uncountable set of infinite things OR the powerset of Aleph-0. Aleph numbers continue on. With Aleph-2 being the powerset of Aleph-1 and so on and so on.

In other systems, such as the hyperreals that I mentioned above, 2ω is a bigger infinity than ω, and ω^2 is bigger than 2ω. This different because with Aleph Numbers, "Aleph-0 + Alephh-0 = Aleph-0" and "Aleph-0 * Aleph-0 = Aleph-0"

It can get confusing when the site uses infinitesimals and also Aleph numbers when they don't go together.

 

[Georredannea15]

First of all, is this a question and answer or is it to change the standards? Because right now the standards don't treat the two the same.

Being infinitely greater than infinity is equivalent to adding infinity to infinity or multiplying infinity by infinity and it's the same degree of infinity. "This does not mean greater mathematical infinity in its context"

Like, infinite x 4D is just 4D.
Infinitely larger in general doesn't get you to Low 1-C whether from Low 2-C or from 2-A. You need qualitative superiority and then it's the case for both.
Proving qualitative superiority is where you might find differences. Being infinitely larger than a 2-A space is certainly better supportive evidence than just being infinitely larger than a Low 2-C space. However, it's not a sufficient criteria.

In the context of being infinitesimal, it is called a mathematically inaccessible set. But it is not like the difference between an infinite structure and a finite structure.

In normal English, infinitesimal means “something that is extremely small”, but in mathematics it has an even stronger meaning. It is a quantity that is infinitely small; so small as to be non-measurable.

Non-measurable set is explained here

In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume". The mathematical existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory. In Zermelo–Fraenkel set theory, the axiom of choice entails that non-measurable subsets of �

exist.

Here is another explanation.(I borrowed it from someone)

In short, the two are very different things in context. In the context of "infinitely greater than infinity" it's just adding or multiplying infinity by infinity and it doesn't mean greater mathematical infinity, but infinitesimal means a subset within itself and that's greater mathematical infinity

So infinitely larger than infinity<<< seeing infinitesimal= greater mathematical infinity

And if you have a statement like "greater mathematical infinity than this infinity", it gives you N+1 without much question.

In short, this "non-measurable" actually means that what a structure cannot achieve through repetition within itself (in set theory), it can never achieve what is above it.
For example, if a finite structure repeats itself infinitely many times, it can reach an infinite structure, so this is not technically "non-measurable" and infinitesimal.

 

[Fixxed]

Perceiving something as infinitesimal does not make something infinitesimal. Take two objects, A and B. If A is infinite in size, and B is finite in size, I have seen people say things like, "B is infinitesimal to A". That's not true. B is not infinitesimal and will never be infinitesimal no matter how big A is. Finite and infinite things can never be infinitesimal. Sure you may be be able to get away, "perceives as" but that's just hyperbole, subjective, or a metaphor and not reality.

And someone can correct me if I am wrong, but this site uses Cantor's set theory and Aleph numbers. Infinitesimals are not apart of that system. So it really confuses me that people are using infinitesimals in conjunction with set theory and aleph numbers, and bigger infinities.

There is a number system, the hyperreal system that incorporates infinitesimals and infinites. But these infinites are different from the infinites in set theory and aleph numbers and cannot be used as a one to one exchange. For example in the hyper reals, ω represents infinity. And you can 2ω and ω+1, and ω^2 and so and so on, and those are all distinct values of infinity, and someone can correct me if I am wrong, can have bigger or smaller values than each other.

But to answer your questions:

Infinitesimals are not equal to any infinity. They are smaller than any finite positive number including any real positive number. Your example of 0.999 is not an example of an infinitesimal.

"Infinitely larger" depends on what you are comparing. Any infinite value is infinitely larger than any finite value. I am not sure if finite values are infinitely larger than infinitesimal values, but someone else can answer to that.

"Bigger infinity" depends again on the type of math you are talking. In set theory, what this site uses, Aleph-0 represents a countable set of infinite things. A bigger infinity would Aleph-1 which represents an uncountable set of infinite things OR the powerset of Aleph-0. Aleph numbers continue on. With Aleph-2 being the powerset of Aleph-1 and so on and so on.

In other systems, such as the hyperreals that I mentioned above, 2ω is a bigger infinity than ω, and ω^2 is bigger than 2ω. This different because with Aleph Numbers, "Aleph-0 + Alephh-0 = Aleph-0" and "Aleph-0 * Aleph-0 = Aleph-0"

It can get confusing when the site uses infinitesimals and also Aleph numbers when they don't go together.

Well the wiki is use higher infinity and infinitesimal interchangable. Higher infinity=perceiving as infinitesimal

Tier 1: Extradimensional
Characters or objects that can significantly affect spaces of qualitatively greater sizes than ordinary universal models and spaces, usually represented in fiction by higher levels or states of existence (Or "levels of infinity", as referred below) which trivialize everything below them into insignificance, normally by perceiving them as akin to fictional constructs or something infinitesimal.

And i dont understand what the mean of "perceiving as infinitesimal doesnt make something is infinitesimal"

What i want to talking in here is about the 1/infinite basically, infinitesimal is something that divided to infinity

Basically i argue about infinitesimal thing go to finite thing. I just think, logically it must have have infinitely bigger size for the infinitesimal to the thing it self, because infinitesimal is be obtained from divided infinitely so it must "united the piece" infinitely or yeah getting bigger infinitely

Yeah i know bigger infinity will have uncountable infinity, i just confusing because the site use infinitesimal equal to bigger/higher infinity

 

[Fixxed]

First of all, is this a question and answer or is it to change the standards? Because right now the standards don't treat the two the same.

Being infinitely greater than infinity is equivalent to adding infinity to infinity or multiplying infinity by infinity and it's the same degree of infinity. "This does not mean greater mathematical infinity in its context"

In the context of being infinitesimal, it is called a mathematically inaccessible set. But it is not like the difference between an infinite structure and a finite structure.

Non-measurable set is explained here

Here is another explanation.(I borrowed it from someone)

In short, the two are very different things in context. In the context of "infinitely greater than infinity" it's just adding or multiplying infinity by infinity and it doesn't mean greater mathematical infinity, but infinitesimal means a subset within itself and that's greater mathematical infinity

So infinitely larger than infinity<<< seeing infinitesimal= greater mathematical infinity

And if you have a statement like "greater mathematical infinity than this infinity", it gives you N+1 without much question.

In short, this "non-measurable" actually means that what a structure cannot achieve through repetition within itself (in set theory), it can never achieve what is above it.
For example, if a finite structure repeats itself infinitely many times, it can reach an infinite structure, so this is not technically "non-measurable" and infinitesimal.

Where you get infinitesimall=non measurable???

Because if you read in here, it is no word saying about non measurable

Infinitesimal - Wikipedia

en.m.wikipedia.org

So i ask you the source about your argument?

In short, the two are very different things in context. In the context of "infinitely greater than infinity" it's just adding or multiplying infinity by infinity and it doesn't mean greater mathematical infinity, but infinitesimal means a subset within itself and that's greater mathematical infinity

And i must ask you the source of this argument??? Bruh every infinity is same because it have same size. I literally say bigger in size. Infinity bigger than infinity

 

[Iamunanimousinthat]

And i dont understand what the mean of "perceiving as infinitesimal doesnt make something is infinitesimal"

Infinitesimal is a set value. It will be the same no matter what you compare it too. So when people say, "This layer is so large, it sees the universe as infinitesimal", it doesn't make sense, because the universe has a set value that isn't infinitesimal. Bigger infinities do not make finite things or even smaller things infinitesimal.

And i dont understand what the mean of "perceiving as infinitesimal doesnt make something is infinitesimal"

What i want to talking in here is about the 1/infinite basically, infinitesimal is something that divided to infinity

Basically i argue about infinitesimal thing go to finite thing. I just think, logically it must have have infinitely bigger size for the infinitesimal to the thing it self, because infinitesimal is be obtained from divided infinitely so it must "united the piece" infinitely or yeah getting bigger infinitely

Yeah i know bigger infinity will have uncountable infinity, i just confusing because the site use infinitesimal equal to bigger/higher infinity

It's because the site uses Aleph numbers for its infinite sizes. This is a contradiction with infinitesimals, because infinitesimals use a different system of infinity.

 

[Fixxed]

Infinitesimal is a set value. It will be the same no matter what you compare it too. So when people say, "This layer is so large, it sees the universe as infinitesimal", it doesn't make sense, because the universe has a set value that isn't infinitesimal. Bigger infinities do not make finite things or even smaller things infinitesimal.


It's because the site uses Aleph numbers for its infinite sizes. This is a contradiction with infinitesimals, because infinitesimals use a different system of infinity.

So why the wiki use that for get tier???

I think the wiki use them interchangable, as the standard literally say, perceiving something as infinitesimal is equal to higher/biggee infinity

 

[Iamunanimousinthat]

So why the wiki use that for get tier???

I think the wiki use them interchangable, as the standard literally say, perceiving something as infinitesimal is equal to higher/biggee infinity

It has to do with "qualitive superiority".

The wiki shouldn't be using both infinitesimals and aleph numbers together. They contradict each other.

You can gain a tier for viewing a universe as being infinitesimal but at the same time you have staff saying that being infinitely bigger than a universe doesn't gain you a tier.

 

[Georredannea15]

Where you get infinitesimall=non measurable???

Because if you read in here, it is no word saying about non measurable

Infinitesimal - Wikipedia

en.m.wikipedia.org

So i ask you the source about your argument?

And i must ask you the source of this argument??? Bruh every infinity is same because it have same size. I literally say bigger in size. Infinity bigger than infinity

I've given you the context and sources for the meaning of this infinitesimal. If you take a little trouble to read it, you'll understand

Infinitesimal means very small in English, but in mathematics it means "non-measurable".

 

[Fixxed]

It has to do with "qualitive superiority".

The wiki shouldn't be using both infinitesimals and aleph numbers together. They contradict each other.

You can gain a tier for viewing a universe as being infinitesimal but at the same time you have staff saying that being infinitely bigger than a universe doesn't gain you a tier.

Well it is weird. Because if the two system is different we just can use logic for them, if you wanna make them interchangeable

 

[Fixxed]

I've given you the context and sources for the meaning of this infinitesimal. If you take a little trouble to read it, you'll understand

Infinitesimal means very small in English, but in mathematics it means "non-measurable".

No i ask for the source of where the infinitesimall is mean non measurable. I not ask for what is non measurable mean

What you give is just a explanation about non measurable, but not give the proof of non measurable is infinitesimal

 

[Georredannea15]

It has to do with "qualitive superiority".

The wiki shouldn't be using both infinitesimals and aleph numbers together. They contradict each other.

You can gain a tier for viewing a universe as being infinitesimal but at the same time you have staff saying that being infinitely bigger than a universe doesn't gain you a tier.

Because the two are not the same thing in the context.

Infinitesimal means "non-mearusable" in the context , and it's not like a simple "difference between a finite and an infinite structure, or between a structure that sees an infinite structure as finite". Because it can get there by repeating within itself.


Being infinitely larger than an infinite structure is no different than "infinite + infinite" or "infinite x infinite", they are still the same infinities.

infinitesimal means a subset but it's not the same with "being infinitely larger than an infinite structure."

 

[Georredannea15]

No i ask for the source of where the infinitesimall is mean non measurable. I not ask for what is non measurable mean

What you give is just a explanation about non measurable, but not give the proof of non measurable is infinitesimal

I have already given the source, I have nothing more to add. In the thread that is going on right now, the staffs has already made statements about these things, but wait for them again if you want

 

[Fixxed]

I have already given the source, I have nothing more to add. In the thread that is going on right now, the staffs has already made statements about these things, but wait for them again if you want

Your source is just explain what is non measurable?? Where is infinitesimall=nonmeasurable???

Or where the source of this quote???

In normal English, infinitesimal means “something that is extremely small”, but in mathematics it has an even stronger meaning. It is a quantity that is infinitely small; so small as to be non-measurable.

Where the source of your argument???

Even your argument about infinitely bigger size than infinity is contradict with the explanation in wikipedia it self that say the infinities is different in size

Just show me your source

 

[Benimōru]

No i ask for the source of where the infinitesimall is mean non measurable.

This I guess

 

[Iamunanimousinthat]

Because the two are not the same thing in the context.

Infinitesimal means "non-mearusable" in the context , and it's not like a simple "difference between a finite and an infinite structure, or between a structure that sees an infinite structure as finite". Because it can get there by repeating within itself.


Being infinitely larger than an infinite structure is no different than "infinite + infinite" or "infinite x infinite", they are still the same infinities.

infinitesimal means a subset but it's not the same with "being infinitely larger than an infinite structure."

That's not accurate. An infinitesimal is a number that is greater than 0 but less than any real number.

Under the hyperreal number system that incorporates infinitesimals, infinity is written as: ω. And under that system ω + ω = 2ω and ω*ω = ω^2.

It's a completely different system of infinity that set theory.

 

[Georredannea15]

That's not accurate. An infinitesimal is a number that is greater than 0 but less than any real number.

Under the hyperreal number system that incorporates infinitesimals, infinity is written as: ω. And under that system ω + ω = 2ω and ω*ω = ω^2.

It's a completely different system of infinity that set theory.

There is no difference between them anyway. The situation here is "inaccessibility", which also occurs in set theory. This actually means that sets cannot be reached by repeating each other, and the continuum hypothesis is considered. So yeah, different statements, but same contexts.

 

[Iamunanimousinthat]

There is no difference between them anyway. The situation here is "inaccessibility", which also occurs in set theory. This actually means that sets cannot be reached by repeating each other, and the continuum hypothesis is considered. Different statements, but same contexts.

There is a difference between. Under the hyperreals, ω^2 > 2ω > ω. Infinitesimals are not apart of set theory.

 

[Fixxed]

This I guess

I dont know where that site found that explanation, but yeah it explain about infinitesimal in calculus, just like the infinitesimal that i brought in here

 

[Georredannea15]

There is a difference between. Under the hyperreals, ω^2 > 2ω > ω. Infinitesimals are not apart of set theory.

In this case it's the same, in fact that's what i means.

For example aleph 0 x aleph 0 or 2 aleph 0 is no different from aleph 0. This is in the same context as being "infinitely greater than an infinite structure, and it is still the same degree of infinity."


If it is infinitesimal, it is like aleph 0^aleph 0 in the context, this is aleph 1 and in this case aleph 0 is infinitesimal.

Btw instead of ^2, you should write ^infinite. Because for that you have to have an infinite exponent

Edit: Lmao you already wrote 2^infinite, mb

 

[Georredannea15]

I dont know where that site found that explanation, but yeah it explain about infinitesimal in calculus, just like the infinitesimal that i brought in here

So yes, as I said, they are very different in context.(being infinitely larger than an infinite structure and seeing infinitesimal)

 

[Fixxed]

So yes, as I said, they are very different in context.(being infinitely larger than an infinite structure and seeing infinitesimal)

No bruh, infinitesimall is not set theory. What the site explain is about infinitesimal in calculus, the example is jonh wallis' theory that say infinitesimal is 1 divided by infinity

 

[Georredannea15]

No bruh, infinitesimall is not set theory. What the site explain is about infinitesimal in calculus, the example is jonh wallis' theory that say infinitesimal is 1 divided by infinity

After all the sources and explains I have quoted, you are still spouting the same nonsense. You never get tired of being wrong lmao

 

[Iamunanimousinthat]

In this case it's the same, in fact that's what i means.

For example aleph 0 x aleph 0 or 2 aleph 0 is no different from aleph 0. This is in the same context as being "infinitely greater than an infinite structure, and it is still the same degree of infinity."


If it is infinitesimal, it is like aleph 0^aleph 0 in the context, this is aleph 1 and in this case aleph 0 is infinitesimal.

Btw instead of ^2, you should write ^infinite. Because for that you have to have an infinite exponent

It's not the case. They're two different systems.

 

[Georredannea15]

It's not the case. They're two different systems.

The functioning is different, but the logic and context are the same.

 

[Fixxed]

After all the sources and explains I have quoted, you are still spouting the same nonsense. You never get tired of being wrong lmao

All the sources?? Bruh i dont know where the site found that, i search "is infinitesimal is nonmeasurable" is just show that site and just that site only that say that. The site also not explain why the infinitesimal is connect to the non measurable set, it just explain the infinitesimal in calculus

If that is your source ok

But it literally mention and explain about infinitesimal in calculus not in the set theory

 

[Iamunanimousinthat]

The functioning is different, but the logic and context are the same.

Dude. They're not. It's two different logic systems.

Under Hyperreals, ω < 2ω < ω^2. (they're each different infinites)

While under set theory infinity = infinity + infinity = infinity * infinity. (they're all the same infinities)

 

[Georredannea15]

All the sources?? Bruh i dont know where the site found that, i search "is infinitesimal is nonmeasurable" is just show that site and just that site only that say that. The site also not explain why the infinitesimal is connect to the non measurable set, it just explain the infinitesimal in calculus

If that is your source ok

But it literally mention and explain about infinitesimal in calculus not in the set theory

Bro are u smoking or what? This is already the meaning in mathematics and set theory

 

[Georredannea15]

Dude. They're not. It's two different logic systems.

Under Hyperreals, ω < 2ω < ω^2. (they're each different infinites)

While under set theory infinity = infinity + infinity = infinity * infinity. (they're all the same infinities)

Yes, that's exactly it. That's what I'm trying to say lol

Being infinitely larger than an infinite structure is no different than "infinite + infinite" or "infinite x infinite", they are still the same infinities.

 

[Fixxed]

Bro are u smoking or what? This is already the meaning in mathematics and set theory

No, i just care the credibility of that site. I can show you some site that literally say uncountable infinity is infinitely larger than infinity. But i sure you will ask the credibility of that size because thats not why you believe

 

[Fixxed]

Bro are u smoking or what? This is already the meaning in mathematics and set theory

And calculus is not set theory

 

[Fixxed]

Yes, that's exactly it. That's what I'm trying to say lol

I think what you say is infinitesimall is in set theory that is non measurable set. That what you wanna say, right??

 

[Georredannea15]

No, i just care the credibility of that site. I can show you some site that literally say uncountable infinity is infinitely larger than infinity. But i sure you will ask the credibility of that size because thats not why you believe

Because the things mentioned there are generally "mathematical infinity" and its direct context is mathematics, but the authors do not use it in this sense. If he is already using it, he specifically states this.

 

[Fixxed]

Because the things mentioned there are generally "mathematical infinity" and its direct context is mathematics, but the authors do not use it in this sense. If he is already using it, he specifically states this.

No bruh i ask the credibility of that site. Because i already search "is infinitesimal is nonmeasurable set" in google, i not found any other thing that say about that unless that site. That site also not explain why the infinitesimal is in the set theory, it only explain about infinitesimal in calculus