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Math Philosophy-- Why does 1/∞ not equal 0, and for that matter, what is ∞?

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posted on Mar, 19 2012 @ 07:18 PM
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Originally posted by XtraTL
reply to post by djeminy
 


I'm not sure what is so special about the facts you quote that they should not be taught in Universities. We teach them pretty well at the University I am at.

All of the facts are trivialities to do with the decimal expansion of rational numbers. If you google it, you will find it is not a secret, and certainly taught at many Universities.

Or maybe you think that you can patent the actual numbers you have in your list, and then universities won't be able to teach about them.

(As a friend of mine jokes, "there are many copyright and illegal whole numbers".)



Looks like you read other peoples posts the same way the devil eats ice-creams!

First you misquote me, and then you give comments to your own 'misquote' .....brilliant!

I said that it's NOT being taught in schools, not, that it should NOT be taught in schools! Big difference.

Try asking your teacher what's so special about 1/1.225125, or so special about 1/24642, and he/she would look at you as if you got a screw loose.
On the other hand, if you knew the answer to these questions, it would be the teacher who would feel a bit on the inadequate side, one should think!

Next time, please quote verbatim and in context, as this will save a lot of time - please!

Cheers




posted on Mar, 19 2012 @ 07:45 PM
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reply to post by PhysicsAdept
 



We may just have to agree to disagree. Your proofs aren't proving anything, and although I think mine are pretty good, you are stubborn enough not to move your position


I just flat out disagree.

You start off wrong by trying to use infinity numerically. You have backed off a bit by saying it is a concept and not a number...but then you continue and say "but you can use it numerically". NO...you can't.

My proofs are simple and basic definitions and facts.


It is not that I don't get the concept of infinity, it is that you say infinity cannot be reached. I say it can. I do not know how, or when but it must exist somewhere at sometime, perhaps at all time. BUT, that must mean we can treat it as a plane, no? Try proving to me that 0 exists--it too is a concept that many people mistreat and misunderstand.


No..infinity can not be reached...else it is no longer infinity.

Can you stop an unstoppable force? Can you move an immovable object? Can you reach infinity?

The answer is the same to all three questions.

All "numbers" are concepts...but they are concepts that we have classified as "numbers". Zero isn't a counting number, but it IS a number.

If you want to go the route that zero isn't a number either...then good luck in math.



posted on Mar, 19 2012 @ 07:52 PM
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reply to post by PhysicsAdept
 


1/INFINITY = 0

EXPLAINED

AS YOU MAY NOTICE IF THE NUMBER X FROM 1/X IS INCREASED THE EQUATION= LESS AND LESS, AS INFINITY IS JUST THAT INFINITE THAN ANY NUMBER OTHER THAN INFINITY DIVIDED BY INFINITY=0.
AS THE NUMBER X GETS LARGER IT WILL APPROACH 0 WITH ANY NUMBER OTHER THAN INFINITY, INFINITY THEREFORE GETS IT THERE AS IT IS JUST THAT INFINITE.

REMEMBER INFINITE IS A CONCEPT, NOT AN ACTUAL NUMBER.

IT IS HOWEVER VERY USEFUL.
The equations in statistics were worked out with infinity. Infinity was used to work out things like; what is a reasonable sample size when not knowing the size of population it is taken from. If you did this with n then you would have to know n to work out your equations, with infinity used to produce these equations you do not.

edit on 19-3-2012 by s12345 because: (no reason given)



posted on Mar, 19 2012 @ 07:57 PM
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reply to post by PhysicsAdept
 



Well this may be a horrible example, but remember, we are dealing with indeterminates. So let us say that 1/0=∞. It is a vertical line and has a slope, also of some undefined amount. But then, rearrange the equation and you get 1/∞=0. Unless you would like to dispute this by saying 1/0 equals 1(0r). That is among the same principle you are using


1/0 does not equal infinity.

It doesn't matter how many times you post it...it isn't correct. 1/0 is undefined.

1/infinity is also undefined.




The easiest way I can show you this is by assuming you are correct and showing you the paradox it creates.

So let's assume 1/infinity = 0. That would mean 1 = infinity * 0.

But I'm sure you would also say 2/infinity = 0...which would mean 2 = infinity * 0.

Simple replacement gives you 1 = 2.


It just doesn't work...and you or the other guy saying this works out have yet to address this...because you can't...because it breaks all known math laws.


I don't know any other way to say it...you are dancing around the fact that what you are trying to say is 1=2...or 32=1987...or x = y for all positive integers where x and y are different values.



Until you can come up with a good answer to this paradox...I see no reason for me to continue to bang my . against a brick wall that refuses to budge.



posted on Mar, 19 2012 @ 07:59 PM
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No 1/0 is just undefined on your calculator in actual fact in mathematics it is infinity as 0 goes an infinite amount of times into 1, or any other number for that fact.


also

0/anything is 0.
edit on 19-3-2012 by s12345 because: (no reason given)



posted on Mar, 19 2012 @ 08:03 PM
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reply to post by PhysicsAdept
 



don't think he is confused at all, I think that must be you. Or perhaps a little bit of everyone, myself included. You keep saying ∞ is not a number so don't treat it like one. So you cannot conclude 1=2 by this logic. We are saying that you cannot treat ∞ as a number either, but yet you can still use it in some numerical sense like 1/∞=0. Now here is a question for you... You say that 1/∞=.0r1, right? Then obviously 2/∞=.0r2? Or do you keep true to your sense of ∞ here and say that 2/∞=.0r1 in which case, you are saying 2=1.


Honestly...at this point I think it's useless.

Infinity is a concept...but YOU are using it as a number. You can say that you aren't, that you are only using it "in some numerical sense"...but that is the same thing as using it as a number. You are just saying it differently. It's like saying...I'm not stealing from you...I'm just removing your items from you possession. Honestly...take a second....and read this statement over and over and please see how nonsensical it sounds "infinity is a concept , not a number, so we can't use it as a number. But we can use it in a numerical sense."

I have never said 1/infinity = 0.0r1...I said that if you MUST break the concept and use it as a number, that would be closer to the truth than zero. But it's not...because 1/infinity is UNDEFINED.


All I know is that you are going to have a very hard time in higher level math courses if you continue to confuse your mind like this. You have a thread of people telling you that you are wrong...many with much more knowledge and education in mathematics than you have...and you just continue to say "nope...I'm right".

It's ok to be wrong...it's not ok to refuse to admit when you are wrong.



posted on Mar, 19 2012 @ 08:14 PM
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Originally posted by s12345
No 1/0 is just undefined on your calculator in actual fact in mathematics it is infinity as 0 goes an infinite amount of times into 1, or any other number for that fact.


also

0/anything is 0.
edit on 19-3-2012 by s12345 because: (no reason given)


1/0 is undefined.

sorry...it just is.

If you think otherwise...explain this.

1/0 = x

1 = x * 0

1 = 0

Or just go a. and replace infinity in there

1/0 = infinity

1 = infinity * 0

infinity * 0 is an indeterminate...but it is not equal to 1.



posted on Mar, 19 2012 @ 08:19 PM
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not to over simplify.... but

to limit infinity is a gross oxymoron and probably the root of the paradox of your 1/∞ = 0

the moment you include ∞ in your equation everything else becomes irrelevant

1/∞=∞
∞*1=∞
x/∞=∞
∞*x=∞
therefore x=∞

and ∞+1 is ≥ AND ≤ ∞



just my ∞^2


edit on 19-3-2012 by Majestyka because: video




posted on Mar, 19 2012 @ 08:27 PM
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This is turning into a circus.

The Mathematical Menagerie.

I think a lot of people missed the point of the 0.9r=1 example so I'm going to have another crack at explaining it.

Infinity is a concept.....useless for anything except describing the universe/creator........maybe....maybe its not even good for that.

We can imagine a concept like infinity but we cannot calculate anything with it, no matter how hard we try.

For example take the value/expression 1/3

Expressed as a decimal gives us 0.3r ...that is....we have a decimal point followed by an infinite line of threes.

No human/computer/calculator can calculate an infinite line of 3's.....it is simply impossible.

First we must change our infinite expression to a finite expression.

If we use a calculator or computer to perform an operation with our 0.3r , it will change the value to 0.3333333.

In the example we showed that 3 x 1/3 = 1

We know that 1/3 = 0.3r

However, if we try to perform the operation with our rounded - fixed to workaround infinity answer...

3 x 0.33333333

Our answer can only ever be 0.99999999

We can never get back our perfect one because we had to round to work around infinity.

This example is used primarily to show students the value of fractions but it also demonstrates the problems associated with trying to calculate a value with an infinitely recurring remainder.

In calculus we allow a variable, usually an x or u - when range permits - an infinite range of values.

We can't calculate an infinite range of values for x as it would be a Cartesian graph that went on forever. We merely select an appropriate range for the operation at hand and plot our graph to suit.

1/x has an asymptote at zero because the value of x can never actually be infinity.



posted on Mar, 19 2012 @ 08:27 PM
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reply to post by Majestyka
 


My reply

1/∞=∞
no it equals 0


∞*1=∞
correct that is just saying infinity =infinity multiplied by anything but 0 = infinity

x/∞=∞
depends upon x if x= infinity then it = 1 if not then it = 0

∞*x=∞
obviously anything multiplied by infinity except 0 =infinity

therefore x=∞
no completely wrong.

If you do not know what you are talking about please do not confuse the discussion.

and ∞+1 is ≥ AND ≤ ∞
aba what , infinity +1 =infinity


just my ∞^2
obviously infinity

however infinity to 0 power =1
edit on 19-3-2012 by s12345 because: (no reason given)

edit on 19-3-2012 by s12345 because: (no reason given)



posted on Mar, 19 2012 @ 08:35 PM
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reply to post by OccamAssassin
 



1/x has an asymptote at zero because the value of x can never actually be infinity.


Good luck getting them to understand this.

I think I'm about done with this thread. I enjoy talking about math when people will listen...when people want to learn...but when people don't want to learn we are literally just running in circles.
edit on 19-3-2012 by OutKast Searcher because: (no reason given)



posted on Mar, 19 2012 @ 08:43 PM
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reply to post by s12345
 


0=∞

0 is just a placeholder infinite nothingness is still nothingness nonetheless





If you do not know what you are talking about please do not confuse the discussion.


i understand the infinite.... you cannot define ∞
the moment you do it ceases to be ∞



posted on Mar, 19 2012 @ 08:53 PM
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From Wikibooks
en.wikibooks.org...


Infinity is not a number.

Mathematics is based on formal rules that govern the subject. When a list of formal rules applies to a type of object (e.g., "a number") those rules must always apply — no exceptions!

What makes infinity different is this: "there is no number greater than infinity". You can write down the formula in a lot of different ways, but here's one way: 1 + infinity = infinity . If you add one to infinity, you still have infinity; you don't have a bigger number. If you believe that, then infinity is not a number.

Since infinity does not follow the rules laid down for numbers, it cannot be a number.



SO.......if infinity is not a number putting it into the formulas you guys are posting / arguing about, makes no sense !

Not that I know anything, but that makes more sense than what you guys have spent ...... how many pages now ?



posted on Mar, 19 2012 @ 08:59 PM
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The infinite part of 1 is neither 1 or 0, that is the whole point

Infinity is not a number. It is force, or call it a principle, a direction, a sense, but it is not a sum which can be expressed.



posted on Mar, 19 2012 @ 09:03 PM
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reply to post by PhysicsAdept
 


Ahh, but that is the beauty. Now keep in mind we can have both less than zero, a need or a pull by some force, known or unknown, and we can have more then zero, an excess. These conditions we know we can grasp but what about zero? If we reached a true/absolute equilibrium what would happen. Would all cease to move and thus exist? I mean what keeps everything moving is the need for something it does not have: the sun, black holes, our moon, our solar system, our action potentials, our breath, our heart, our universe is moving because zero has not been reached, everything and anything exists because there is no equilibrium...yet. So, yes there is no entropy in zero for no exchange of any force or energy under any condition is needed in the state of zero.
Sorry but I love using molecular condensation as an example. so when the molecules are cooled to a point close to absolute zero they begin be unified, they work together but remain individual. they are no longer aware whose protons, neutrons or electrons are whose. when in this state they change our current understanding of object, light, space, matter, anti-matter etc. they become very close to an equilibrium, they become so static that light no longer can react in normal ways. refraction, reflection, transference mean nothing. It is as if the closer those molecules get to zero the more they cease to exist. And I feel this applies to all scales of measurement, no matter what, zero is an equilibrium and at that point what is being measured no longer can supply any data except that zero has been reached, currently....that is until we figure out how to pass through dimensions (though this is pure theory on part and perhaps a bit whimsical, although I am currently running with it)



posted on Mar, 19 2012 @ 09:07 PM
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reply to post by OutKast Searcher
 


Tsk tsk. Well alas I believe we are at an impasse. I greatly enjoyed everyone's ideas including yours. I cannot admit that I am wrong because I have yet to see how I am wrong. The problem with this question, "Why does 1/∞ not equal 0", or really it has involved into "What does 1/∞ equal", is that no one wants to deal with infinity. I tried to make my point, loud and clear, that we were assuming we could reach infinity.

Here is where the problem is.

Everyone (I generalize, nut not completely conclude it is EVERYone) with an education, as well as everyone without an education, does not seem to want to step out of the box for a second. The question is not what the limit is, nor what it means... well to an extent it is, but the real question and analysis is supposed to come after the point of infinity is reached. Now, my stance here is that, who knows if it is possible?

I know the definition of infinity, please do not insult me by saying I don't (or that I am missing fundamental skills, or that cannot grasp a limit). However, as a mathematician, I feel like it is (our) obligation to explore! It is (our) obligation to delve into the unknown and try to find out as much as we can!

Well, I get excited from it anyway. I mean, to just decide infinity as something that doesn't belong in an equation... it hurts a little bit. If infinity truly does represent everything, should we not attempt at the very least to incorporate it into an equation here and there? Mind you, it is not a number, but I stand by what I say! I wish to examine it as a number, as if it were one, as well as if it was this unstoppable force colliding into an unmovable object. Where is the harm in that? Infinity to me must act differently that the typical number though, because unlike the rationals, it is not constant. Unlike the irrationals it has no estimated definition. THAT is what I wanted to discuss. I want some speculation every now and again. Trust me, I am all about the numbers. I am the first guy to ask for the statistics of something and the math behind reasoning. But I have yet to see any undeniable proof of what you say, sorry.

Your proofs have been just as valid as mine in some ways, and also just as contradictory. Like on the other thread when you were talking about units... and how units are not generalizations, because they aren't exact they are based on society. Uh, yeahhh hello that would be a generalization.

Anyway, I wanted to explore what happened to that limit once x did in fact equal infinity. Remember, there is no proof to say it cannot happen, just speculation backing that it cannot. Because absence of proof is not proof of absence I chose to ascend into the chaotic realm of indeterminacy. I guess some people do not belong here--the textbooks cannot help them which must bring fear into their mind, clouding their vision.

With everything (I can currently think of) being said, I would like to point out that I do not believe you are wrong. Your entire purpose it seems is to prove that you are right. I will agree in front of all of ATS that I believe you to be correct, and this is why:




There is no such point to where you can not divide it further in math theory.

In reality, it depends on what you are talking about...and in reality things are finite, not infinite.


True, in the real world that is true. We live in the real world, and thus it is true. However, I think this quote helps my case more than yours, outside of the real world. In reality, things are finite, not infinite. I wasn't walking about reality, I was talking about sub-reality. Ya know, where the plane of infinity exists. The imaginative side of math, that maybe one day can be an application for the real world. (Imaginary numbers where originally thought of as nothing useful but apparently used in circuitry today under practical application. Bet Descartes would have freaked
)

So I hope now, that maybe you can step back and see my side. You, in reality, are correct. I will admit to that (though I dare you to try to find a quote of me refuting that, with respect to reality).

So reality aside, I want to ask you. No explanation is needed, if you say no then I will already understand why you say it. If you were to reach infinity, outside of what we hypothesize to be true in the real world, does 1/∞=0?
edit on 19-3-2012 by PhysicsAdept because: (no reason given)



posted on Mar, 19 2012 @ 09:12 PM
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reply to post by athes
 


Yes it sure does give you a vast wealth to think about... Perhaps after everyone refuels their mind and takes a break I will post my theories on absolute zero--one of my favorite topics. In short, a prelude to the thread I hope to author soon-- I believe the universe itself would cease to exist in time as we know it. Equilibrium would have to occur at a universal level, and nothing would be able to escape it. The universe would remain temperatureless, and thusly motionless. As for all the unaccounted--energy, that is where the debate shall begin.



posted on Mar, 19 2012 @ 09:27 PM
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Originally posted by OccamAssassin
reply to post by MeesterB
 


Exactly!

*insert applause*

To add
Does 0.9r = 1 ?


Hi all. I too love maths, so the big problem here is that infinity is a concept, not an absolute value, so cannot technically be put into an equation. The whole 1/0 = infinity thing is a bit of a fallacy. As for the above quoe; yes 0.9999...................... etc does equal 1!



posted on Mar, 19 2012 @ 09:29 PM
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reply to post by UKLionheart
 


Would you say then, that .000000000000000000000000000000...1 equals 0?



posted on Mar, 19 2012 @ 09:35 PM
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reply to post by PhysicsAdept
 


You said in your opening post that some infinites are larger than others. This is true. There are "countable" and "uncountable" infinities.

For example:

1 2 3 4 5....
1 4 9 16 25....

You can count the square numbers, but you cannot count decimals, because there is always another decimal place to add. you can however count fractions!!

Here is a really interesting documentary on infinity:
www.youtube.com...



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