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

I can't help wondering that if you took a real object and divided it by infinity, that eventually you would turn space-time inside out

reply to post by PhysicsAdept
Do you think mathematicians should distinguish between the type of infinity that represents the number of rational numbers between, say, any two integers, and the infinity one reaches (or does not reach) traveling to either end of the number line? If so, would it make sense to refer to these different kinds of infinity as “internal” and “external” or by some other term?

If such a distinction already exists, forgive me for asking such an uneducated question.

Nothing can reach 0, because 0 doesn't exist.

1/∞ would never equal zero, you would get extremely close to zero but would never reach it because there would always be a number that would divide 1; something would always be present.
Zero is a very special value. it is not a point nothing, it not the absence of something, it is not the representation of emptiness or lacking of anything. if it did all numerical values would not continue beyond zero. Zero is the moment of equilibrium. it represents the point in time, mathematically, when all of space, atoms, molecules, quarks, particles, time, life, temperature, weight, etc. etc. are in complete equilibrium; at least absolute zero does, but our zero does this on a smaller scale. Think about absolute zero, molecular condensation, and volatile solutions.
The true power of zero is not taught in the early math classes. We are told that having no apples equals zero, but we aren't told that this means it is an apple equilibrium with the environment. Some how there were once apples and now there are none. Why? well maybe someone ate them over time, or maybe an equal number of people each ate an apple or they went bad and were tossed, it really does not matter. what does matter is that at some point there were apples present which caused an imbalance in that space (consider the nutritional need filled by the apples for people) the imbalance caused the need to consume the apples or they began to rot and caused a greater imbalance and the urgency to balance the space grew, lol. Again in either circumstance Zero truly does not represent the lack of something but it does represent an Equilibrium.

reply to post by PhysicsAdept

You can divide by zero, it happens all the time. With l'hopital's rule it is always welcomed in concept. Also this, idea of not dividing by 0 comes back to infinity not being able to be reached--mere speculation that cannot technically be proven nor disprove except through more concept and speculation. SO for our purposes in the original thread, we assume it CAN be.

I will have to see some examples of dividing by zero happening all the time, I still stand by that it can't happen.

Because if x/0 = y, then you have to somehow come up with how y * 0 = x where x is a positive integer.

Infinity, by definition, can't be reached because it is boundless. This is like the old physics paradox of what happens when an unstoppable force meets an unmovable object. If you start to try to explain how the unstoppable force would be stopped by the unmovable object...you have breached the definition of an "unstoppable" force.

Same with infinity, once you start saying "when infinity is reached", you have breached the definition of "infinity" and are no longer using it correctly.

sinx/x evaluated at 0 produces an indeterminate (infinity) so it is difficult to say that this example really works. Yes the limit does not correspond with the "plugging in" of 0, but it produces something else that could mean many different things (theoretically even 1, who knows)

Indeterminate does not equal infinity.

If the limit does not correspond with "pluggin in" of 0, then the limit of 1/x where x approaches infinity also does not correspond to "plugging in" of infinity.

You have just admitted your whole premise does not work.

If you divide something you ALLWAYS have at least two parts.

Originally posted by PhysicsAdept
reply to post by OutKast Searcher

 

Has to do with rates is my guess. You cannot just multiply each side by infinity to resolve that 1=2.

Ok seriously, last post of the night, more tomorrow

Why not?

So now not only is infinity a number, but it is a number that has different values at different times? And it doesn't follow basic algebra rules?

reply to post by circlemaker

0*1 = 0. 0*2 = 0. This works fine too. There's no paradox. Think of numbers in terms of distance from the origin (typically 0).

So in your world....100 = 1 and 45 = 0 and 32 = 98????

I'm sorry...but I have to say you are more confused than anyone else in this thread. I would suggest that you take some formal courses instead of just teaching yourself...easy to confuse yourself to the point where valid mathematics will never make sense to the incorrect world view you have built in your mind.

If you divide any finite number an infinite number of times, the resulting length or distance (from 0) is still 0.

It will never be zero...and you can never divide it an infinite number of times.

Like the OP...if you claim you can....you are breaking the definition of infinity.

Infinity isn't a large number...it is a boundless boundry.

reply to post by PhysicsAdept


The day the teacher started putting letters into the equations was the day I learned for sure that someone along the way either was lying to me or had lied to me. That was the day I began to divorce math.

But I can appreciate the way you think none the less, PhysicsAdept.

Irony? Throughout my firefighter career in the usaf ... let's just say people would be suprised how much math firefighters have to know and memorize.

reply to post by PhysicsAdept


1. You are gifted, no doubt
2. You are gifted to ask the questions you ask.
3. You have a great teacher
4. Your links make me grasp the whole limits stuff a little better.

Originally posted by OutKast Searcher
So in your world....100 = 1 and 45 = 0 and 32 = 98????

Umm no. Did you read what I said? Did you even BOTHER to try and understand it?

I'm sorry...but I have to say you are more confused than anyone else in this thread. I would suggest that you take some formal courses instead of just teaching yourself...easy to confuse yourself to the point where valid mathematics will never make sense to the incorrect world view you have built in your mind.

How is this helping? Are you trying to provoke me? Geometry doesn't lie. The proof is there in the pictures I posted for those who care to take the time to understand. Just because it goes against conventional mathematics doesn't make it wrong.

No wonder I despise academia. "If it's not in a textbook it doesn't exist", right?

Originally posted by OutKast Searcher
It will never be zero...and you can never divide it an infinite number of times.

Like the OP...if you claim you can....you are breaking the definition of infinity.

Infinity isn't a large number...it is a boundless boundry.

You're limiting yourself with preconceptions. Peek outside your box every once in a while and you might actually learn something.

reply to post by circlemaker

Umm no. Did you read what I said? Did you even BOTHER to try and understand it?

All you said is that if you multiply 1 and 2 by zero...they both equal zero so there is no paradox.

But there is...and I think you are just avoiding it.

There is no way around this.

In your world:

1/infinity = 0

2/infinity = 0

since 0=0, we can replace

1/infinity = 2/infinity

Multiply both sides by infinity and you get

1 = 2

I can do this for any set of numbers...which is why I said in your world view, things like 32=98 are true.




This is basic algebra.

Originally posted by circlemaker

Originally posted by OutKast Searcher
It will never be zero...and you can never divide it an infinite number of times.

Like the OP...if you claim you can....you are breaking the definition of infinity.

Infinity isn't a large number...it is a boundless boundry.

You're limiting yourself with preconceptions. Peek outside your box every once in a while and you might actually learn something.

Yes, I am limiting myself with definitions...how dare I.

I can make some outrageous claims to if I decide to ignore definitions...like I claim that I can fly...but I define flying as no part of my body touching the ground...so everytime I jump I fly



Tell me this...what has breaking concepts done for you? What has your made up math done in real life? I know you have created a bunch of graphs...but what real world applications does your made up math give us?


I'll give you some advice as you have given me...stop making things up, and maybe you will actually learn useful things that can be used in the real world.

I haven't read all the posts yet, but:

lim ∞/∞ (or -∞/-∞) is not possible, nor is 0/0, ∞ x 0 etc.
x ->∞

You have to use l'hospital there and derive the functions.

btw
lim 1/x = 0
x->∞

limes means that the function gets closer to... (in the case of 1/x) to 0, but does not mean it IS 0.

Originally posted by OutKast Searcher
In your world:

1/infinity = 0

2/infinity = 0

since 0=0, we can replace

1/infinity = 2/infinity

Multiply both sides by infinity and you get

1 = 2

That's completely nonsensical. Both sides of what?

You're treating infinity as if it's a finite (but very large) number with polarity. It doesn't work like that. I've already explained how this works but you claim that a finite number can't be divided an infinite number of times and that's where you stopped thinking.

there are two concepts in our reality that don't exist that is true randomness and infinity.

reply to post by circlemaker

That's completely nonsensical. Both sides of what?

You're treating infinity as if it's a finite (but very large) number with polarity. It doesn't work like that. I've already explained how this works but you claim that a finite number can't be divided an infinite number of times and that's where you stopped thinking.

I agree...it is completely nonsensical...all caused by you claiming anything divided by infinity equals zero.

I am not treating infinity as anything...you and the OP are trying to treat it as a number that you can use mathematical operations on.

YOU say that:

1/infinite= 0

Well what is the answer to this:

1/finite = ?

or

1/large = ?



YOU are treating a concept (infinity) as a number...and I'm telling you that you are wrong. I'm showing you are wrong by the paradoxes it creates. And yet you are saying that is is ME that is using infinity as a number and that is non-sensical....we seriously just went in a complete circle.

The arguing you are all witnessing in this thread is the battle between philosophical objective math and practical application math...they can't explain each-other so it is pointless to try.

Practical application math has no use for concepts such as infinity, and uses the concept of zero merely as a godlike placeholder to illustrate a point of transition of +/- measurements. Infinity for practical math is usually disregarded because it creates some serious problems...practical math cannot accurately describe or produce a wall that is infinitely high....there is no point or purpose for such a thing from a practical standpoint.

Philosophical math has no use for practical math because it acknowledges the concept of infinity which makes all numbers arbitrary and pointless....

they are like oil and water...they don't mesh. This is why people struggle with infinity they try to work with it in a context that makes no sense and they try and try to force it to make sense when its not supposed to. They try and combine oil and water and go back and forth in frustration at the same time making contradictory claims.

reply to post by PhysicsAdept


This has got to be one of the dumbest threads i have ever read.

Infinity is not a number. Therefore, subbing it into algebraic equations is completely useless.

Infinity is a concept. You cant divide a number by a concept...

1/infinite = nothing (not zero... nothing)

This is pretty basic 11th grade logic. Im extremely surprised to see 2 threads like this on the front page within 2 days.

only on ats, i suppose