Meanderings : 7,000 posts

[Black Mage]

Zero times infinity would be zero

I can see your reasoning there, as normally any number times zero equals zero.  But I am seeing things differently.  I am seeing zero as the reciprocal of infinity.  This makes perfect sense because the reciprocal of a number that is very close to zero (10^-100, for instance) is a number that is very close to infinity (10^100).  Since any number multiplied by its reciprocal equals one, zero multiplied by infinity must equal one.

At first it seemed as if the result should be undefined, because it simply seemed logical that zero times infinity could conceivably equal any real number, but now it seems to make more sense when the result is one.

but if o is the reciprocal of infinity
using
oo for infinity

0 = oo^-1
0 = 1/oo
but
0 != 1/oo

on a side note:
oo^-1 == 10E-oo == 0.000000[infinite amount of zeros]0000001

[Grimm]

I'd never see zero as the reciprocal of infinity. I can understand if its Zero = Nothing, Infinity = Everything, but in the end, anything multiplied by zero is still zero.

Also, technically infinity isn't a number, its just the idea that numbers continue on forever. So technically we can't use infinity in math, atlhough I know we do (sum of an infinite sequence, for example).

[a civilian]

I don't see why should infinity be regarded as any less of a number than zero.  Both are equally immeasurable.

[Grimm]

Actually, zero seems pretty easy to measure. Take a measuring cup, for example, and... let it sit there. You have zero! Unless you count the air in it, which I am not counting for this example.

[a civilian]

But that is measuring zero in terms of zero; assuming its existence.

[Keyser59]

Could you elaborate on that a little bit?

Infinity is not a tangible number. 0 is. Look at the graph of f(x) = 1/x. According to your reasoning (I believe) f(0) = oo/-oo. How does it make sense that for one x value the graph as two values? We all know that this is a function, so such a statement has to be false.

BTW you can't get close to infinity. We sometimes use high numbers to try to predict limits of different functions, but it is impossible to replace infinity with a high number.

[Decimator]

So much controversy over infinity....

[a civilian]

Infinity is not a tangible number. 0 is. Look at the graph of f(x) = 1/x. According to your reasoning (I believe) f(0) = oo/-oo. How does it make sense that for one x value the graph as two values? We all know that this is a function, so such a statement has to be false.

Then perhaps infinity and negative infinity are the same.  I have thought about this too, and it makes perfect sense to me.  Starting with 2/2 (1), and subtracting from the denominator, 2/2, 2/1, 2/0, 2/-1.

BTW you can't get close to infinity. We sometimes use high numbers to try to predict limits of different functions, but it is impossible to replace infinity with a high number.

The way I see it, infinity and zero are equally difficult to reach.  Infinity may be impossible to reach by simply increasing a number, but that is akin to simply increasing the denominator of a fraction in hopes of reaching zero.  To reach zero, you must subtract from the numerator.  Similarly, to reach infinity, you must subtract from the denominator.


But perhaps this is all only my misguided desire for elegance.  I find this possible symmetry between zero and infinity to be irresistible.

[JHunz]

Zero times infinity is zero.  Infinity divided by infinity is still infinity, believe it or not.  Or that's what I remember from calculus, anyway

And the problem with your reasoning, civilian, is that zero is a well-defined number.  The problem with infinity is that by definition it cannot be well-defined.

[BobTheJanitor]

I can see infinity divided by itself still being infinity. Put something infinite into something infinite, and it will go in an infinite number of times. However, infinity times zero is still infinity??? That makes no sense. Anything, zero times... is still zero. Was that a typo, or true? And if true, how the HELL...?

[JHunz]

I have no idea what you're talking about

[BobTheJanitor]

OMG MOD HAX. You could have at least fixed your other typo:

believe it or not

Quoting that a lot so that when you go back and re-edit your post you will then have to re-edit mine several times over to make yourself look good again.  But I didn't reckon on your keen intelligence making a fool of me

So hah!

<3

[size=8]Last edited by BobTheJanitor, 6:30 PM February 25[/size]

[Keyser59]

Infinity divided by infinity is a undefined term the same way that 0/0 is undefined. If you have to find the limit of such an equation like f(x) = (3x^2 + 5x)/(9x^2) as x approaches infinity, it would merely be 1/3.

You can't use infinity without limits because infinity is not a tangible number, and can't be substituted in normal algebra. 2/0 does not equal infinity. 2/0 has no solution because no matter how large a number you multiply 0 by, you will never reach 2, or any positive number.

To understand that you must realize that 0*oo does equal 0. Unless you've discovered a new branch of mathematics there is no way you can change that.

[a civilian]

To understand that you must realize that 0*oo does equal 0. Unless you've discovered a new branch of mathematics there is no way you can change that.

The product of zero and infinity being an undefined number is indeed the premise for my arguments, but I do not see why that must be untrue.  Perhaps I have, then, discovered a new branch of mathematics.

[Keyser59]

Your logic defies basic reasoning. You have to understand that 1/oo is an infinitly small number. It does not equal 0, but it approaches 0. You can't say infinity equals anything because it is not a number.

This can be demonstrated by plugging in increasing numbers. You'll obviously see the trend that that the result gets smaller and smaller.

However, according to you 0 * oo approaches an undefined number. This is not true.

If you plug in ever increasing numbers, you get the same result each time, and the trend shows that this function approaches 0. No matter how infinitly high you make x, y will always be 0.

Granted, when you say 1/oo is 0, I assume you talk about limits, because it is impossible to pull real numbers out of any function with infinity.

[a civilian]

You mention plugging in increasingly large numbers to simulate infinity.  But this does not work.  I would liken it to plugging in increasingly small fractions in an attempt to simulate zero.  Infinity is an infinitely large number, and cannot be reached by simply counting upwards.

[Grimm]

I have never actually seen infinity as a number. I've always seen infinity as something continuing on and on and on and on forever, basically.

[Keyser59]

So why can't you plug smaller and smaller numbers to simulate 0? How does that not work?

[a civilian]

Take division of zero by zero.  Replace the zeros with x, and plug in any number other than zero or infinity for x.  The result is one.  But is that the same [edit - or, to word it better, indicative of the] result that would be achieved by dividing zero by zero?  It is not; as you stated previously, zero divided by zero is undefined.

[Keyser59]

That is the one oddball example where nothing really holds true, just because of the fact 0 divided by 0 is undefined.

In pretty much every other example this holds true. If f(0) = 3, the closer and closer your x values come to 0, the closer and closer your f(x) values will come to 3. Unless you have a jump discontinuity, the value of a function will always be the same as the limit.

My whole point is you can never find values for functions involving 0 in the denominator or oo. You can however find limits. Saying that 1/oo is 0 is absurd, because oo by definition is an undefined term.

I find your treating of infinity like a number is quite odd. Infinity is not a number and cannot be used in algebra in any way shape or form. Infinity is a term used to describe an infinitly increasing number, which can be used in calculus.