Zero Divided by Infinity = All possibilities?

[JustBusiness17]

This thought originally came out of the idea that "everything came from nothing" which seems to be a central debate no matter what level of regression your beliefs allow you to envision. This topic is probably better categorized under philosophy, although I wanted some professional mathematicians to tell me where I might be wrong...

So, without necessarily assuming there was a "beginning" to anything, I'm starting this thought experiment at zero. Rather than thinking of zero in its traditional sense (that of being nothing) we can actually think of zero as being infinitely vast in its nothingness. You might assume that an infinity of nothingness is still nothing, although that assumption overlooks the incomprehensible nature of infinity. Georg Cantor was one of the first to really embrace the concept of infinity for what it really is, which is limitlessness within limitlessness taken to infinity. It's a difficult concept to struggle with which is probably why Cantor went insane...

A concept that I can't seem to shake (and if you detect a flaw, please elaborate) is the idea that zero divide by infinity allows for all possibilities. Consider 0/1=0, 0/2=0 ... , all the way up to 0/∞=0. Regardless of the denominator, 0 divided by anything is still zero. But, taking into consideration the limitless nature of infinity, zero divided by infinity creates limitless possibilities for something within nothing.

I bolster this point with the idea that physicists speculate that sum over all energy within our own universe is actually equal to zero. The positive balances the negative which makes us a null equation. If you take the nothingness of our universe and insert it into one of the infinite fractions of zero, the equation still balances to zero.

Just so that people can wrap their heads around this concept, I'm suggesting that something may be possible when you take 0/∞/∞/∞/∞/∞/∞/∞/∞/∞..../∞. Zero may be nothing, but when examined on an infinitely small scale, there is always the possibility for something...


(Please put this idea to rest because it's been bothering me for a while...)

 

[nemesiss]

the problem lies in the properties of both [infinite] and zero;
they have no boundries.

inifity is infinite large while zero is infinite small.

when you try to divide between them you get answer which ranges from;
-infinite to +infinite, which means you have no real answer.

hence why it's an unknown

 

[Master_Ghost_Knight]

First of all what is division? You will be shocked to know that division doesn't realy exist in mathematics. :shock: As a complete operand.
When you have a real number "A" (for instance 4, 5, whatever) and another "B", when you devide B by A. B/A, you are not (in mathematics) really deviding B by A but you are rather multiplying B by another number C for which AC=1 (C a.k.a. 1/A or the inverse of A, know by the axiom of inverse). And zero doesn't have a number D for witch 0D=1. This is why devision by zero is not defined, in the same way 1/inf isn't exactly defined because inf is not a number, even tough for a finite "K" lim(x->inf) k/x has a value by continuity and that value is zero (and therefore we very often say 1/inf =0 without breaking a sweat) while lim(x->0) k/x doesn't. Of course from this you can define your operand division and describe it in the way you are most familiar with but it drags with it the problem that the division by certain numbers isn't simply defined (among other problems). (subtraction sufers of a similar condition but doesn't cause this sort of problems, it causes others)

Secondly what exactly do you mean with what you are saying? When we use mathematics in science they are at least parts of models that describe and quatitize something, it allow us to relate something that we can measure (directly or indirectly) and be able to predict something else that we can measure, like the force of gravity, the energetic relations, the equations of motion that can for instance given a object traveling at a certain speed (that we can measure) tell us how far can it go (which we can measure) from a planet with a certain mass (that we can measure). And this allows us to say concrete things, to say that 0/inf has a profund relation to the universe without ever specifying what that relation is, what is it supoused to relate or what is it that you are quantifying is simply meaningless, much less being able to say if what you are using to describe is valid at a certain circumstance even less so if it is valid in the circumstance you are using it to describe whatever it is you want to describe.

It is an interesting thing trying to conceptualize this things and makes up for good practice, but don't get your hopes up on thinking that it means more than just that.

 

[JustBusiness17]

I may have been top dog in high school, but they never taught us anything about axioms in the curriculum (at least not that I remember... I was never really good with focus ). I don't think you've entirely put my idea to rest, but it seems like you've positioned it pretty good for a death blow.

My intention for "dividing nothing by infinity" isn't so much about actually solving an equation, but rather to create a mental model for understanding how nothing can contain something. In order to survey an area for observable evidence of something, the best approach would be to break it into a grid. The smaller the scale of the grid, the more accurate the survey. By taking an area and dividing it by infinity, I'm essentially creating a grid small enough to ensure that I assess the entire area accurately. The area in this particular circumstance happens to be quite small :arrow: Infinitely small :?

In that sense, dividing zero by infinity isn't so much about producing an answer as it is about creating a framework for observation. Reality seems to exist... The question I'm asking is whether it exists inside of one infinitesimally small fraction of zero or many...

Here's an image to help illustrate the idea. Imagine that there is nothing inside of this grid. In order to actually prove that nothing exists within the grid, I would have to examine each square to ensure that nothing exists within it. To be truly accurate in my survey, I would have to take each square and section it off into a similar grid. Taking squares from a grid and dividing them into a new grid is a process that would have to be repeated into infinity in order to actually prove that nothing is there. But if you found "something" inside an infinitely small square of nothing, is it not small enough to still call the entire entity "nothing"?

Does that better explain my approach better?

 

[JustBusiness17]

 

[JustBusiness17]

Further to that point, does infinity divided by infinity not equal 1?


(On a side note, I'm starting to understand why Cantor went insane :? )

 

[Unwardil]

I love the hotel model of infinity.

I have a hotel with infinite rooms and they are all full.

Someone comes in looking for a room, so I move everyone who's already booked in into the next room and then there's space.

An infinite number of buses full of and infinite number people come to the hotel and not only do I make room in my already full infinitely sized multi level parking lot by moving everyone on even numbered levels to odd numbered levels, but the same trick works for for the rooms too.

What tends to boggle the mind about infinity is that we're very used to numbers signifying real things and in the context of infinity, the actual size of the number is irrelevant in context to the whole.

 

[nemesiss]

Further to that point, does infinity divided by infinity not equal 1?


(On a side note, I'm starting to understand why Cantor went insane :? )

thats why you can't use it like a normal integer

[infinite] +x = [infinite]
[infinite] - x = [infinite]
[infinite] * x, where x!=0 = [infinite]
[infinite] / x, where x!=0 = [infinite]

 

[Nelson]

Further to that point, does infinity divided by infinity not equal 1?

Not necessarily. There are different types of infinities (see Continuum Hypothesis).

And in general infinity/infinity is not necessarily equal to 1. Here are a few examples:

In all of these cases the top or bottom of the fraction evaluated alone is equal to infinity, but the two functions do not necessarily describe the same sort of infinity. They approach it at different rates if you like to think of it that way. At infinity, e^x grows infinitely faster than x does. Conversely, at infinity x grows at 1/4 the rate that 4x does.

 

[Master_Ghost_Knight]

I may have been top dog in high school, but they never taught us anything about axioms in the curriculum (at least not that I remember... I was never really good with focus ).

Well they don't teach that in high school period, that is why I always say that you really don't learn any math until you get to college

My intention for "dividing nothing by infinity" isn't so much about actually solving an equation, but rather to create a mental model for understanding how nothing can contain something.

Well you won't get it this way because 0/inf has a known limit and that limit is 0. That settles that. Neither do I hold that space is infinitely divisible, the continuous space hypothesis holds amazingly well at large scales (and it is what we are familiar with the day to day experience) but space can still be fundamentally discrete (and we can demonstrate mathematically that at large scales some discrete solutions are virtually undistinguishable from continuous ones, and those that are not you very often get models derived from quantum mechanics).
But here is something that I use to contest with physicist (other physicists that I know contest it as well) in respect to terminology, because I like to use a strict definition of void and many physicist don't do that. "Well what about the energy of the void?" you may ask. And the general objection is, "well if it has energy then it is not really void in the sense that there is absolutely nothing there" now there is nothing wrong in not existing "void" (in the strict use of the word) in the universe if that turns out to be the case. Now the "nothing" has sort of the same problem, some people use it in the strict since and others not so much, but even though I would contest that the case for our universe has literally come from the strict use of the word nothing has been made let's assume for the sake of argument that this is literally our case (which is a default position, it is something that we know it must be right, we just can't show you why).
How then can something really come from nothing?
Well imagine that you are in a flat plain, no hills no holes no anything, it is completely flat. How then can you make a hill without borrowing any sand? It's simple, you make a hole as well, you are borrowing sand from the hole to build your hill. Now instead of plains you have nothing, and instead of hills and holes you have positive energy and negative energy. (yeah I have cheated a bit with the sand example because there is sand so something already exists, but I can't explain it in terms that are familiar to us but I hope you get the point). You can also see it partially as words, in a sense you don't have a sort of bag inside of you storing the words you speak (and if for some reason you speak allot of them you run out of it) in a way the words just become when you speak it.
Of course I am not saying that the universe is fundamentally like this, neither do I think that universe is anything like it appears to be. Space for instance maybe just a property that objects hold, like temperature and it maybe that when we move back and forward is like we are just getting colder or warmer, and when you perceive to get close to something and push it might just be like you are able to raise the temperature of something else if your temperature is a certain amount close to that something else (our perception of space is just an illusion caused by our senses, in reality it may be nothing like it at all). And there is nothing wrong with this model of the properties of the world not being what appears to our senses, a it makes absolutely no difference what so ever if it translates exactly in to the phenomena in the way we perceive it. In the same way as living in a computer it makes absolutely no difference in the phenomenological happenings if the world is real or just a electrical impulses being transmitted about producing what it appears to be the physical world.
(in a way my temperature example was fortunate because it is a good example of something that isn't what we perceive to be, there isn't an intrinsic property called temperature, temperature is just about how fast particles are moving around; but there are others things that do a similar things).

You can entertain these things, and conceptualize worlds that are extremely bizarre (so bizarre that you may not even be able to explains in things that we can conceive) and yet be completely consistent with what we observe and satisfyingly simple.

Of course everything that I have just said isn't exactly science (at least yet), it is fun to entertain this things but we must not forget that I was duealing in pure speculation and etertaining this for the sake on thinking on them.

In a way that makes me remember of a creationist objection, "How can you trust your brains?"
And for me the answer to that is fundamentally simple, you can't, we know that we can't, we always doubt our senses all the time by using better instruments to do things and the more we explore things the more we know that reality is counter intuitive. It is only a matter of how much you can get away with getting consistent answers while your brain is tricking you in the wrong way.

:arrow: Infinitely small :?

The word you are looking for is "infinitesimal".

 

[Gunboat Diplomat]

You'd better stick with marketing, JustBusiness17, 'cause this argument makes no sense!

A concept that I can't seem to shake (and if you detect a flaw, please elaborate) is the idea that zero divide by infinity allows for all possibilities. Consider 0/1=0, 0/2=0 ... , all the way up to 0/∞=0. Regardless of the denominator, 0 divided by anything is still zero. But, taking into consideration the limitless nature of infinity, zero divided by infinity creates limitless possibilities for something within nothing.

Are you sure you don't mean 0 * ∞ = x, where x represents "all possibilities?" Even if ∞ were a number with which you can divide, 0 divided by it will surely still equal zero. I'm not sure why you're wanting to divide zero and your grid diagram is not elucidating anything...

Further to that point, does infinity divided by infinity not equal 1?

Again, assuming ∞ is a number with which you can apply arithmetic operations, there are different kinds of infinity, some of which are larger than others. What do you suppose those quotients will be?

In fact, with seemingly reasonable definitions of division, using the same reasoning that Unwardil explained, I can show you that ∞ / ∞ will still equal ∞...

Sadly, I'm late to this game and others have said all this already but I'll throw my two cents: ∞ is a concept and not a number with which you can apply arithmetic operations. It is a property that certain sets have or a direction you can follow. Your poor characterization of it is what allows you to come to these poor conclusions...

 

[JustBusiness17]

LoL... I feel like I'm in the strange position of being both underestimated and overestimated at the exact same time :?

@MGK

I'm familiar with the concept of a zero sum universe and actually referred to it in the OP. Based on my secondary level of math, physics, and calculus from 10 years ago, it seems to make sense to me, but as you say, anything beyond postulation is meaningless at this point.

The interesting thing is that what I'm postulating isn't necessarily incompatible with that idea. While this may simply be an indication of my struggle to comprehend dimensions beyond the 4 macros, my approach to this is more out of practicality in the same sense as your sand-hill example. In a sense, I'm placing a "coordinate" on the empty plain where our little "sand-hill" happens to exist.

Rather than continuing with the concept of a grid, let me present it from a different perspective. IF you could observe a void (in a very slightly less strict definition of the word (in which case void may not be the correct word)) and you had limitless abilities in your observation, hypothetically, you could "zoom-in" on the void to explore what exists within it. If you magnified it by a power of 2, you would still see an empty void. If you then magnified it by another factor of 2, you would see the same result. What I'm saying is that if you continued to increase the magnification by factors of 2, the precision of your observations would increase exponentially. Assuming you look in the right "place" with a magnification strength approaching infinity, you would eventually find the plain (or "brane" as I understand it) with the "sand-hill" that we call our universe.

But as you say, despite the existence of the anomaly, its not really there because the energy balances out to zero. So despite finding "something" within the void, the definition is not entirely corrupted based on the zero-sum of the anomaly. Additionally, despite what we perceive as being an infinitely large universe, the anomaly is really only an infinitesimal entity within the void, so small that the void's integrity as such remains intact.

The essence of what I'm saying is that when you examine "nothing" on an infinitesimal scale, it should be no surprise that you find "something".

Is this concept seriously that far out that its somehow beyond refinement?

 

[Master_Ghost_Knight]

Ok let's give it another go.
So what you rae saying that your model of things is more like c=m/v (concetration of things equals mass or proprety devided by space) and you have m=0 (zero mass or some proprety) and you zoom in space to inf and thus you get 0/inf?
Well if this is the case (because I am not entierly sure what you mean) then I don't think your conceptualised equation is describing what you want to say. Becuase if you devide your unit of volume infinitey then v=1/inf and when you replace v in the equation c=m/v (while m=0) what you get is c=0/(1/inf) = 0*inf (and here is something that we are familiar with that can be non zero).
However this has a tiny bitsy problem, we all sort of use an unriten law of science that the real world happenings is indiferent to the scale you are looking at it (while being an absent observer), so the fact that you are "zooming in" shouldn't realy change reality. If you can't see it at an arbitrary scale then you can't see it at any way you use to get there (srange thing this notion that we expect the propreties to distort and become completly different as you move into extreme scale conditions). Of course I would also contest that space is infinitly divisible but that is something I can live without, but perhaps we are forgeting that space itself didn't exist at some point and this way of thinking maybe completly out of context with reality.

Ok, I think this topic should now belong to the phylosophy section. I do remember myself when I was youger and less educated and I spent days on trying to visualize how can the inner working of reality be so it seams the way it is, what is the default position that something with certain propreties should have. Later I get more educated and for my surprise allot of things turned out to be right with what we know about today (except now I have a proper way to describe it mathemticaly and in ways that people can understand, we can do experiments to observ it and see that that's the way it is), of course other things not so much, somethings turned out to be almost inconcievably different by quite a better picture than what I had, and there were other things that I haven't even tought of but were so bizzare that I was convinced that they couldn't be right (even tough they always give correct answers) until I wrestled with it for a long time and realised that it had to be right after all.
It makes good practice to think in ways that are not familiar with our day to day experience because reality isn't like our day to day experience, and because you have that mental elasticity you are able to better apreciate things that are simply incomprehensible for most people. So I will leave you at that.

 

[/b/artleby]

I wanted some professional mathematicians to tell me where I might be wrong...

Pretty much the whole thing. Your grammar wasn't too bad though...

Edit: By the by, all of this should have been explained to you in the first week of Calc class, when everyone was reviewing the definition of a limit. In short, you're making two simple mistakes.

1. You're confusing 0/x with the indeterminate case 0/0.
2. You're confusing addition and subtraction with division. x + (-x) = 0, which is essentially the boiled down version of how the entire universe could have on average "zero energy". Division doesn't really have anything to do with it.

Also, randomly throwing continued fractions at something doesn't make it turn into a mathematical marvel...

You could try moving it to the Philosophy section, but I would suggest building a new section for stuff like this called "you really should have payed attention in math class before pretending to be a mathematical philosopher". Really, if you want to learn about continuity and infinity, you should probably pick up a book on Georg Cantor instead of asking an online forum to teach you basic Calc.

 

[mat_hunt]

One way you could tackle this without problems is use the idea of limits. You examine the ratio of a/b say, and then examine the limit as a tends to zero and b tends to infinity.

 

[lrkun]

Nothing can't be divided by something. To illustrate:

0/a or 0 divided by A. In reality it looks like this. divided by A. The thing before divided by is not there.

 

[Master_Ghost_Knight]

Nothing can't be divided by something. To illustrate:

0/a or 0 divided by A. In reality it looks like this. divided by A. The thing before divided by is not there.

Who said that zero is nothing.? Zero is most absolutly not nothing. Nothink is a completly different entity on it's own which is not a number.

 

[lrkun]

Nothing can't be divided by something. To illustrate:

0/a or 0 divided by A. In reality it looks like this. divided by A. The thing before divided by is not there.

Who said that zero is nothing.? Zero is most absolutly not nothing. Nothink is a completly different entity on it's own which is not a number.

The symbol zero represents that which is absent.

0 nothing 1 something.

I have 5 apples. Take away 5, how many are left? 0 = none are left.

0 alone is nothing.

10 - no longer nothing, this represents 10 or to follow my previous example, 10 apples.

 

[Josan]

The symbol zero represents that which is absent.

Not neccesairly, it represents the only real number that is neither negative nor positive. (And we are talking about the number zero. It is, after all, a number, don't try to pretend otherwise)

Nothing can't be divided by something. To illustrate:

0/a or 0 divided by A. In reality it looks like this. divided by A. The thing before divided by is not there.

Please don't bring reality into this. We're talking about mathematics, not reality =P

 

[lrkun]

Not neccesairly, it represents the only real number that is neither negative nor positive. (And we are talking about the number zero. It is, after all, a number, don't try to pretend otherwise)

The issue is the title of the thread. zero divided by infinity = all possibilities.