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Does 0 = Infinity?
#11
RE: Does 0 = Infinity?
As always in these discussions, it depends entirely on the definitions one uses. So one can maybe split thie question in the title in two -

1) is 0=infty in the most common definitions used?

2) If not, can one construct a consistent mathematical system in which 0=infty, and what are its properties?

The first is a no. The second is open for discussion. A trivial example would be defininf the symbol infinity to mean the same as the 0 of real numbers. Then 0= infinity, but infinity probably lacks some properties one would like it to have. etc..
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#12
RE: Does 0 = Infinity?
Ah yeah, the sphere! I'd forgotten about that Smile I haven't seen that for years. Thanks Joe! It strange and neat how infinity becomes a single point.

When dealing with numbers infinity is generally used as a limit rather than being plugged into equations like zero can be.

Maths is fascinating. The way certain special numbers turn up can be very surprising. Like pi is commonly related to circles as the ratio of the circumference to the diameter. But it pops up all over the place. Like:

As n tends to infinity, 1/(1*1)+ 1/(2*2) + 1/(3*3) + ... 1/(n*n) tends towards (pi*pi)/6

It's been so long since I did my maths studies...
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#13
RE: Does 0 = Infinity?
(February 22, 2016 at 9:14 pm)Living in Death Wrote: 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.

Almost nothing you say about 0 as a number is true. The first half of your text even seems like complete gibberish. I don't know what you talk about with nothingness and infinite space. What does any of this have to do with the number 0?

0 is an element of the rational numbers, not irrational in the sense mathematicians use the word, it is not a placeholder but an ordinary element of the rational and real numbers. It does have an effect, e.g. in multiplication, 6*0 !=6. The only unusual property it has in the field of real numbers is that division by it is not defined.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#14
RE: Does 0 = Infinity?
(February 23, 2016 at 4:14 am)Alex K Wrote: Almost nothing you say about 0 as a number is true. The first half of your text even seems like complete gibberish. I don't know what you talk about with nothingness and infinite space. What does any of this have to do with the number 0?

0 is an element of the rational numbers, not irrational in the sense mathematicians use the word, it is not a placeholder but an ordinary element of the rational and real numbers. It does have an effect, e.g. in multiplication,  6*0 !=6. The only unusual property it has in the field of real numbers is that division by it is not defined.

I don't think you understand my point. My point is that 0 as an absolute, to say that there is absolutely nothing in existence, would imply an infinite space. As 0 is most commonly defined, it is usually to demonstrate lack of any predetermined element (or, as I suggested later, to act as a suffix for any multiple of ten). As far as my knowledge goes, my understanding of 0 has been that it acts as a qualitative identifier, not quantitative. Also, as I suggested in my original text, what value does it act as; odd or even?
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#15
RE: Does 0 = Infinity?
As a philosophical idea, I've seen flavors of this idea in the Bible: "I am the alpha and the omega" implies that the beginning and end, which are both unfathomable in some sense, can be equated, and also that this equation is one way to look at the apparent paradox in the universe. It's not that infinity and zero are really different-- but that our perspective on them makes them seem so.

Carl Sagan's foundation series has a cute little plot twist on this idea as well. We normally think of a number LINE, but what if a line isn't the right way to represent inifinity? When you change that conceptual geometry, neat stuff can happen. I've probably already spoiled it for you if you haven't read the series. . . but if you haven't read it go read it. Big Grin
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#16
RE: Does 0 = Infinity?
The other comments are correct: 1/0 is undefined. Similarly, the limit of 1/x as x approaches 0 is also undefined. However, if you take the limit of 1/x as x approaches zero from the left or from the right, you get negative and positive infinity respectively

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#17
RE: Does 0 = Infinity?
(February 22, 2016 at 9:14 pm)Living in Death Wrote: 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?
First of all,zero as a concept was first used in India.What do you mean by borders have a value of zero?You need to understand zero did not come into existence to quantify things that do not exist or exist everywhere  .It is used to denote the absence of a given quantifiable entity in certain set of conditions which otherwise exists or may exist in different circumstances.What I can figure out from your post is that you mean zero as a quantity of "infinite nothingness",i.e., it is the absence of everything(everything being infinite non-null set), which is pretty interesting, but I guess that is not what zero was conceptualized for to begin with.Nothingness(absence of everything) does not exist.It is an inconceivable abstract concept that does not have physical significance while zero has physical significance.There is zero doubt in my mind regarding it. Rolleyes

(April 8, 2016 at 4:37 pm)Boltzmann Brain Wrote: [quote='Living in Death' pid='1210739' dateline='1456190041']
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?
First of all,zero as a concept was first used in India.What do you mean by borders have a value of zero?You need to understand zero did not come into existence to quantify things that do not exist or exist everywhere  .It is used to denote the absence of a given quantifiable entity in certain set of conditions which otherwise exists or may exist in different circumstances.What I can figure out from your post is that you mean zero as a quantity of "infinite nothingness",i.e., it is the absence of everything(everything being infinite non-null set), which is pretty interesting, but I guess that is not what zero was conceptualized for to begin with.Nothingness(absence of everything) does not exist.It is an inconceivable abstract concept that does not have physical significance while zero has physical significance.There is zero doubt in my mind regarding it. Rolleyes
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#18
RE: Does 0 = Infinity?
in math each value has only 1 symbol.
0=0 meaning nothing, and can be used as a place holder for something, as it is empty.
∞=∞ meaning perpetually, and can be interpreted to indicate any category of values. It can be used as a placeholder for values also.

to be brief, .999 does not equal 1. only 1=1, and the lack of .0001 is always a difference in 1 and .999
to be quaint.

nothing can exist, indefinitely, but not infinitely. That is would not be a grammatical clause.

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#19
RE: Does 0 = Infinity?
I think the Bible might be saying that 0=infinity: "I am the Alpha and the Omega" seems to equate the two.

Someone said zero is a valid number. Yes, that's true, but not in all contexts, specifically when dividing.

I'd argue that zero and infinity have a kind of inverse relationship. The problem is that when you reverse direction of multiplication/division, you can get really weird stuff:

1/0 = infinity, therefore infinity * 0 = 1;
2/0 = infinity, therefore infinity * 0 = 2;

Therefore 1=2, and all numbers are equal. Clearly, this is broken. However, if you're looking for a goofy philosophical quantity to replace God, then playing with zero and infinity is a pretty good way to "explain" how something comes out of nothing. maybe in the Big Bang singularity, there's no such thing as number-ness, and there is simply a philosophical principle like this one that is meaningless once things unravel into what we'd call reality.
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#20
RE: Does 0 = Infinity?
(February 22, 2016 at 9:55 pm)scoobysnack Wrote:
(February 22, 2016 at 9:14 pm)Living in Death Wrote: 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 don't have time to watch the video at the moment, but it sounds like the divisional problem and is really talking about precision.  With a very small unit of measurement, you will get a very large number, and with a smaller unit, you will have better accuracy.  However, you will always have a finite number.  If it was infinite, then no matter how much time and patience you had to measure to the smallest degree, you would never be able to reach the end.   If it is infinite, then this would also be true, when using larger units.  Similarly some say, that if you divide a number by two (and keep doing so), that you will reach infinity.   While the process may be potentially infinite, by my math, at each division, you will end up with twice the number of points, that you had previously, but at no time, will you reach an infinite number of points.  Unless by infinite, you mean a somewhat common usage of a very large number, and not an actual infinite.

I only had a chance to skim through the video on the recent debate between Professor Grayling and Rabbi Rowe.   But I think that an interesting point that Rowe brought up, is that infinity requires that the thing in question is unbound by nature.  Existential objects (which I am taking to mean physical objects) are necessarily bound by nature.  Therefore, a physical object is necessarily finite.   I'll have to watch the video fully and do some more research, but I found the concept interesting.
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