Is it possible to divide by infinity?

[Obnoxious]

Does x divided by infinity equal to zero? Or is there just no solution.

[JPQuiceno]

Seems to me that it is impossible. Lets call infinty "y" and the number being divided "x". If you do the actual math you have, x/y=?. Since infinity (y) can be anything, it is impossible to get an answer. Please correct me if im wrong.

[Phi for All]

Infinity is not a real number, it's just a representation of an idea.

[Obnoxious]

If infinity can't be a real number, than zero can't be a real number either...As zero is the reciprocal of infinity...

[Tom Mattson]

1. Yes, zero is a real number.

2. No, infinity is not a real number.

3. No, infinity is not the reciprocal of zero. Zero has no multiplicative inverse.

[Dave]

Come on, give it some thought. The natural numbers arise from intuition - you can have twenty apples, seventeen oranges, etc. Zero is a natural extension of this: I could have no apples. So how do you have "infinite" apples? You can't do it.

 

As for the reciprocal stuff... put it this way. The zero element in a set is an element satisfying a.0 = 0.a = 0 for any a. It's pretty obvious that this will be an element of the reals. "Infinity" is just a concept of getting our heads around limits and other useful things. Don't confuse it with actual elements of sets.

[kriminal99]

Any time you see infinity in a math equation just replace it as limit x-> infinity with the x where the infinity was. The subconsious meaning of infinity is "always growing". Therefore writing like 1/infinity is equivalent to saying 1 divided by a value which constantly grows, so really all you can do is take a limit.

 

Where a limit is just to say as x gets closer and closer to a certain value and you have some function of x, then the function will approach some value z until a point where you can no longer distinguish between f(x) and z given a set amount of precision (decimal places you can monitor).

[lepidoptera]

Yes. The answer is infinity. That's like if you had infinite muffins and you said, "Let me give each of these people here the same amount of muffins." There would never be an end to the amount of muffins you would get, so it would be infinite. Infinity divided by anything is infinity.

[Tom Mattson]

Yes. The answer is infinity.

 

No' date=' it isn't.

 

That's like if you had infinite muffins and you said, "Let me give each of these people here the same amount of muffins." There would never be an end to the amount of muffins you would get, so it would be infinite. Infinity divided by anything is infinity.

 

First, that does not answer the question. Obnoxious asked if it is possible to divide by infinity, not if it is possible to divide infinity by some number. Second, an infinite quantity divided by another infinite quantity is indeterminate. Consider the following function:

 

f(x;n)=(xⁿ+1)/(x²+1)

 

Then take the limit as x approaches infinity for n=1,2,3. You will get 3 different answers.

[MathsIsFun]

If x is finite, then x/infinity is "infinitesimal".

 

And, I agree that infinity/infinity is indeterminate.

[matt grime]

Would people at least mind explaining in what ring they are finding the inverse of "infinity" or indeed in what ring "infinity" lies?

 

Would it be better if I phrased it as:

 

1. What do you mean when you talk about dividing by things?

 

2. what are the domains of any binary relations you may wish to define?

 

3 what are the compatibility rules for these operations?

 

4. do you accept you aren't talking about real numbers?

[ydoaPs]

i would think it would be zero. if we take the limit of 1\x as x approaches infinity, won't it get closer and closer to zero as the number gets higher and higher? isn't y=1\x tanget to 0 at infinity? maybe not, i'm not to terribly good at maths beyond algebra 2.

[MathsIsFun]

For all *practical* purposes x/infinity (where x is finite) is indistinguishable from zero, BUT to use it for *mathematics* it needs to be considered infinitesimal.

 

Say we want to calculate the area under a curve, let's divide it into infinite slices and sum up the little mini-areas. The area is the height by the width. The height is the value of the function at that point, and the width is ... ummm ... zero. Oh THATS easy, the area is zero.

 

On second thoughts, lets's make x/infininity=zero. Calculus becomes a lot easier

[Dave]

Ack! You don't seem to be getting the idea. Whilst we all agree that it's perfectly acceptable to define something like [imath]\lim_{x\to\infty} \frac{1}{x}[/imath], it's not acceptable to define things like [imath]\frac{1}{\infty}[/imath].

 

[imath]\infty[/imath] certainly isn't an element of the set of real numbers. It's just a concept, nothing more.

[Anjruu]

Lets look at it, instead of mathematically, theoretically. So, 6/3, is there are six apples, divided into three groups. How many apples are in each group? Two. Now, you have 6/OO. (OO is infinity for this, I don't have spiffy computer infinity functions). So, you have 6 apples, divided into an infinite number of groups. Logically, each group must have an infinitly small piece of an apple. So like, 0.00000000...1 apples. Since this is such a small number, actually, an infinitely small number, we can round it to 0. Anything divided by infinity is equal to zero. Just like MathsisFun said.

 

Wouldnt 00/00 just be 1? Since anything devided by itself is one?

[Ophiolite]

Is it possible to divide by infinity?[/b'].

Yes, but it takes an eternity to do it.......

[matt grime]

If I break down and cry will there be any sympathy? How about I just send my psychiatric bills to you lot?

[Obnoxious]

Well, if you can't divide by infinity, can you at least divide by undefined?

[Ophiolite]

Matt if you deconstruct my statement I think you will see that I am agreeing with you, rather elegantly I thought, 100%. Those who have difficulty with math also seem to have difficulty in reading comprehension. I shouldn't worry - geologists have to deal with creationists- it's worse.

[Dave]

Unless the thread picks up some in the next couple of posts, I'm closing it. There's nothing interesting being generated from this discussion.

[matt grime]

mathsisfun and anjuru were the subjects, not you ophiolite.

[Ophiolite]

That's a relief: irony and arcane humour are sometimes interpreted as stupidity. (Often with good reason.)

[MathsIsFun]

Awww, don't ruin the fun ... this is wonderful stuff.

 

I take the point that infinity is not a real number, but that shouldn't stop us playing with it in relation to real numbers.

 

So, let us slice that apple into infinite pieces and then add up all the pieces to see if we get the apple back again!

 

Yes, we cannot REALLY slice it up like that, but in our minds we CAN.

[Tom Mattson]

Well, if you can't divide by infinity, can you at least divide by undefined?

 

Can you divide by duck?

Can you divide by table?

Can you divide by styrofoam?

Can you divide by blue?

Can you dividy by excited?

 

Of course not. And do you know why? Because none of those things are real numbers. And neither is "undefined".