Does 0 = Infinity?

[Living in Death]

Hi, all. 

This is something which I'd considered a while ago. My logic is a little shaky but my proposition doesn't appear to be too full of holes. 

I guess the principle belief that 0 = infinity would assume that values exist as absolutes. If we were to say that nothing exists, there would be an endless stream of nothing. This was practically the core belief (and, more to the point, revelation) when I was considering this principle for the first time. 

I really don't think my assumption functions in mathematical environments that do not assume absolutes, rather they function as relativistic. In other words, if you have none of something, that doesn't suddenly form a singularity in the space where that something would inhabit. 


My point is that, if we were to create a closed environment involving only a single inhabiting factor, if said factor did not exist (and assuming that this system was an undefined size, eg. the universe), would that not create a space infinitely large? If borders had a value of zero, would they not cease to exist and thus render a potentially infinite empty space? 


I think the reason that this is a difficult problem for me (and maybe for most people, too) is that 0 and infinity are both practically irrational. I believe that the principle of 0 was originally suggested by an Arabic mathematician, but I personally think that it does not infer mathematical properties, rather more philosophical. If we were to hypothetically state that 0 does unarguably equal infinity, it would point towards my two beliefs that, 1. it is not strictly mathematical, 2. it is irrational and thus would not strictly have any place in rational mathematical works (though perhaps hypothetical mathematics). 

Alas, 0 exists as a placeholder for the lack of any element (and of course as a suffix for factors of ten). I see why it is still relevant even today. I suppose my attempts to rationalise it by, ironically, quantifying it with an irrational value is simply my way of showing that it is more complex of a value than we may originally think back in primary, secondary, or even college. 


That's my rant over, at any rate. I'd love to hear everyone else's opinions on the matter. Oh, and perhaps an item of argument; is 0 odd or even?

[Tiberius]

0 doesn't equal infinity, simply because 0 is a valid number, and infinity is not. Infinity cannot be properly placed in any equation, so "0 = Infinity" makes as much sense (that is to say, none at all) as "1/0 = Infinity".

There are numbers which have an infinite amount of digits, for instance 0.111... but if infinity was equal to 0, then these numbers would have 0 repeating digits, which is obviously untrue.

0 is even though: https://en.wikipedia.org/wiki/Parity_of_zero

[SteelCurtain]

Yeah it's a pretty easy contradiction to show inductively, as well.

You can't assume something in a direct proof that is itself a contradiction, namely that zero has no mathematical meaning or purpose. As soon as you assume the negation, you are embarking on proving the contradiction.

EDIT: my bold

[scoobysnack]

Hi, all. 

This is something which I'd considered a while ago. My logic is a little shaky but my proposition doesn't appear to be too full of holes. 

I guess the principle belief that 0 = infinity would assume that values exist as absolutes. If we were to say that nothing exists, there would be an endless stream of nothing. This was practically the core belief (and, more to the point, revelation) when I was considering this principle for the first time. 

I really don't think my assumption functions in mathematical environments that do not assume absolutes, rather they function as relativistic. In other words, if you have none of something, that doesn't suddenly form a singularity in the space where that something would inhabit. 


My point is that, if we were to create a closed environment involving only a single inhabiting factor, if said factor did not exist (and assuming that this system was an undefined size, eg. the universe), would that not create a space infinitely large? If borders had a value of zero, would they not cease to exist and thus render a potentially infinite empty space? 


I think the reason that this is a difficult problem for me (and maybe for most people, too) is that 0 and infinity are both practically irrational. I believe that the principle of 0 was originally suggested by an Arabic mathematician, but I personally think that it does not infer mathematical properties, rather more philosophical. If we were to hypothetically state that 0 does unarguably equal infinity, it would point towards my two beliefs that, 1. it is not strictly mathematical, 2. it is irrational and thus would not strictly have any place in rational mathematical works (though perhaps hypothetical mathematics). 

Alas, 0 exists as a placeholder for the lack of any element (and of course as a suffix for factors of ten). I see why it is still relevant even today. I suppose my attempts to rationalise it by, ironically, quantifying it with an irrational value is simply my way of showing that it is more complex of a value than we may originally think back in primary, secondary, or even college. 


That's my rant over, at any rate. I'd love to hear everyone else's opinions on the matter. Oh, and perhaps an item of argument; is 0 odd or even?

I don't have an answer to your question. Zero considered it can't be divided or multiplied by anything and result in anything else than zero, might mean it's infinite, but I don't have an answer to that.

Something I want to share is a documentary about fractals which talk about infinity. One of the more interesting videos I've seen. Nothing about religion, this was shown to me by my friend who is a member of mensa and super smart. What this talks about is how things are infinitely small, or infinitely big. For example when trying to measure the circumference of a nation, or anything it's infinitely long depending on how close you measure it.

This is a great doc:

https://www.youtube.com/watch?v=HvXbQb57lsE

[Living in Death]

0 doesn't equal infinity, simply because 0 is a valid number, and infinity is not. Infinity cannot be properly placed in any equation, so "0 = Infinity" makes as much sense (that is to say, none at all) as "1/0 = Infinity".

There are numbers which have an infinite amount of digits, for instance 0.111... but if infinity was equal to 0, then these numbers would have 0 repeating digits, which is obviously untrue.

0 is even though: https://en.wikipedia.org/wiki/Parity_of_zero

I personally find that down to interpretation whether it is valid or not. As I claimed before, it appears to primarily indicate a null space. Yet most calculations (at least most that I can conjure up in my mind) either have the 0 allowing a negligible effect or becoming an impossibility (eg. dividing by 0). 

Though mathematics at this level is not particularly my strong suit, so I could easily be making simple work out of a not so simple issue. Your point about the reciprocal decimals is a very strong counter argument, by the way. 

Yeah it's a pretty easy contradiction to show inductively, as well.

You can't assume something in a proof that is itself a contradiction, namely that zero has no mathematical meaning or purpose. As soon as you assume the negation, you are embarking on proving the contradiction.

I agree with you on this. My own negation of the value could well be the cause of my outlook upon it. However, from my experience, 0 appears to have some in common with infinity. Being irrational is only a single component. 

Hi, all. 

This is something which I'd considered a while ago. My logic is a little shaky but my proposition doesn't appear to be too full of holes. 

I guess the principle belief that 0 = infinity would assume that values exist as absolutes. If we were to say that nothing exists, there would be an endless stream of nothing. This was practically the core belief (and, more to the point, revelation) when I was considering this principle for the first time. 

I really don't think my assumption functions in mathematical environments that do not assume absolutes, rather they function as relativistic. In other words, if you have none of something, that doesn't suddenly form a singularity in the space where that something would inhabit. 


My point is that, if we were to create a closed environment involving only a single inhabiting factor, if said factor did not exist (and assuming that this system was an undefined size, eg. the universe), would that not create a space infinitely large? If borders had a value of zero, would they not cease to exist and thus render a potentially infinite empty space? 


I think the reason that this is a difficult problem for me (and maybe for most people, too) is that 0 and infinity are both practically irrational. I believe that the principle of 0 was originally suggested by an Arabic mathematician, but I personally think that it does not infer mathematical properties, rather more philosophical. If we were to hypothetically state that 0 does unarguably equal infinity, it would point towards my two beliefs that, 1. it is not strictly mathematical, 2. it is irrational and thus would not strictly have any place in rational mathematical works (though perhaps hypothetical mathematics). 

Alas, 0 exists as a placeholder for the lack of any element (and of course as a suffix for factors of ten). I see why it is still relevant even today. I suppose my attempts to rationalise it by, ironically, quantifying it with an irrational value is simply my way of showing that it is more complex of a value than we may originally think back in primary, secondary, or even college. 


That's my rant over, at any rate. I'd love to hear everyone else's opinions on the matter. Oh, and perhaps an item of argument; is 0 odd or even?

I don't have an answer to your question. Zero considered it can't be divided or multiplied by anything and result in anything else than zero, might mean it's infinite, but I don't have an answer to that.

Something I want to share is a documentary about fractals which talk about infinity. One of the more interesting videos I've seen. Nothing about religion, this was shown to me by my friend who is a member of mensa and super smart. What this talks about is how things are infinitely small, or infinitely big. For example when trying to measure the circumference of a nation, or anything it's infinitely long depending on how close you measure it.

This is a great doc:

https://www.youtube.com/watch?v=HvXbQb57lsE

I think I know what you're talking about regarding the infinitely large / infinitely small paradox. I read about something similar in one of my books on space; if you were to roughly map Britain, it would come to a value slightly larger or slightly smaller than if you were to measure more accurately. If you got right down to it and measured every last rock, cave and cliff edge, it would come to a very different value than if regarding it as a simple issue and just roughly estimating. However, this must surely end at some point, presumably when we get down to the quantum level of subatomic particles and such. This paradox assumes we can keep going smaller. The question is; can we?

[scoobysnack]

0 doesn't equal infinity, simply because 0 is a valid number, and infinity is not. Infinity cannot be properly placed in any equation, so "0 = Infinity" makes as much sense (that is to say, none at all) as "1/0 = Infinity".

There are numbers which have an infinite amount of digits, for instance 0.111... but if infinity was equal to 0, then these numbers would have 0 repeating digits, which is obviously untrue.

0 is even though: https://en.wikipedia.org/wiki/Parity_of_zero

I personally find that down to interpretation whether it is valid or not. As I claimed before, it appears to primarily indicate a null space. Yet most calculations (at least most that I can conjure up in my mind) either have the 0 allowing a negligible effect or becoming an impossibility (eg. dividing by 0). 

Though mathematics at this level is not particularly my strong suit, so I could easily be making simple work out of a not so simple issue. Your point about the reciprocal decimals is a very strong counter argument, by the way. 

Yeah it's a pretty easy contradiction to show inductively, as well.

You can't assume something in a proof that is itself a contradiction, namely that zero has no mathematical meaning or purpose. As soon as you assume the negation, you are embarking on proving the contradiction.

I agree with you on this. My own negation of the value could well be the cause of my outlook upon it. However, from my experience, 0 appears to have some in common with infinity. Being irrational is only a single component. 

I don't have an answer to your question. Zero considered it can't be divided or multiplied by anything and result in anything else than zero, might mean it's infinite, but I don't have an answer to that.

Something I want to share is a documentary about fractals which talk about infinity. One of the more interesting videos I've seen. Nothing about religion, this was shown to me by my friend who is a member of mensa and super smart. What this talks about is how things are infinitely small, or infinitely big. For example when trying to measure the circumference of a nation, or anything it's infinitely long depending on how close you measure it.

This is a great doc:

https://www.youtube.com/watch?v=HvXbQb57lsE

I think I know what you're talking about regarding the infinitely large / infinitely small paradox. I read about something similar in one of my books on space; if you were to roughly map Britain, it would come to a value slightly larger or slightly smaller than if you were to measure more accurately. If you got right down to it and measured every last rock, cave and cliff edge, it would come to a very different value than if regarding it as a simple issue and just roughly estimating. However, this must surely end at some point, presumably when we get down to the quantum level of subatomic particles and such. This paradox assumes we can keep going smaller. The question is; can we?

Well to be honest I'm not smart enough to answer that. All I can say is can we measure beyond subatomic particles or is that the smallest things are or that we can measure?  For me what interested me what the concept of infinity and whether is it was small or large, yet observed from the human eye as being finite.

The documentary was interesting because it started measuring trees and how to measure a forest based on a tree's growth. This is beyond me, but something I'd like to learn more about.

[Living in Death]

Well to be honest I'm not smart enough to answer that. All I can say is can we measure beyond subatomic particles or is that the smallest things are or that we can measure?  For me what interested me what the concept of infinity and whether is it was small or large, yet observed from the human eye as being finite.

The documentary was interesting because it started measuring trees and how to measure a forest based on a tree's growth. This is beyond me, but something I'd like to learn more about.

That's fair enough. String theory suggests that all subatomic particles may possibly involve tiny strings that oscillate to give them their energy. Whether I believe it or not, it's hard to say. Can't say I'm quite that deep into science myself. 

As for what you say about not being smart enough; I don't think anybody is. Infinity is practically implausible to consider, and the size of particles could simply keep getting smaller and smaller. What are they even going to call particles within subatomic particles? 

Anyway, I think it's interesting what you say; to observe the potentially infinite through a finite perspective and scope. I do think it's crazy that it's very possible for us to do such a thing, if these laws of fractals could be applied in the way they claim they can be of course.

[robvalue]

They are both abstract concepts we use in our attempts to model and understand reality. They perform very different roles.

They are related by

1/n tends to infinity as n tends to zero

[TheRealJoeFish]

They are both abstract concepts we use in our attempts to model and understand reality. They perform very different roles.

They are related by

1/n tends to infinity as n tends to zero

I came on to say essentially this.

To elaborate: although infinity and zero are not equal, the way you're thinking about them and the relation between them is certainly valid in some ways. What you're essentially getting at, I think, is that as 1 is to 1, and 1/2 is to 2, and 1/10 is to 10, 0 is to infinity (that is, infinity represents the multiplicative inverse of zero or vice versa). Although that doesn't exactly work in basic algebra, that thought does have applications in, say, complex analysis and topology. For instance, the Riemann sphere:



This thingy sort of wraps all of the complex numbers onto a sphere (by taking any number on the complex plane, drawing a line between it and the very top point of the sphere, and calling the intersection of that line and the sphere the "projection" of that number). It becomes complete only when you define that top point to be infinity, and, indeed, it does allow you to describe infinity as the multiplicative inverse of zero.

So, yes, they are certainly intricately related as Rob said. Not equal. But... One is the yin to the other's yang. Or something.

[SteelCurtain]

They are mathematically related in the sense you are talking about in that they can be accurately described as limits, or asymptotically.

lim┬(n→∞) 1/n = 0 ∴ lim┬(n→0) 1/n = ∞