Ok this is been debated again and again, now I need to know.

What is 0 * Infinity?
Some say it is undefined.
Some say it is 0.
What do you guys have to say about this?


(for those who say infinity isn't a real number, just pretend it is a number of infinite value.)

I would have said zero but hey......

(for those who say infinity isn't a real number, just pretend it is a number of infinite value.)

Can I just pretend it's a flying pink elephant instead and call it a day?

Read this link:

http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html

it gives a good description of attatching +/- infinity to the reals. It makes sense to define operations with infinity that jibe with the various indeterminate limit forms. With this point of view, you'd leave 0*infinity as undefined, since it could result in anything.

However, some authors will use the convention 0*infinty=0 (that link gives one, Royden is another). This is usually for notational convenience. For example, it will let you multiply a function that takes the value infinity at some locations with a characteristic function and get the answer you'd like. The point is to make the exposition more compact.

You have to realize that by adding +/- infinity to the reals destroys some of the nice algebraic properties of the set. It's no longer a field, so don't expect to be able to do all the algebraic operations on all the elements that you'd like.

Here is what I posted in the other thread.

The other day on the car ride home, I looked at my dads gas meter and saw that is was about half empty (half full). The meter had values labeled with 1/1 and then onto 1/2 in the middle, and then 0 at the end. That got me thinking, the meter was using only lables with 1/x. I was wondering what would x have to be in order for 1/x to be 0. I determined that 1/∞ = 0 since the gas meter was approaching infinity by going from 1/1 to 1/2, and so on, and 0 is at the end. But then an issue came up, what happens when you multiply each side by the denominator? You get 1 = 0*∞. I don't know, you can get vary wierd things when messing with infinity...

(but from what I understand from other things, infinitesimal * infinity (0*∞ ) can equal anything).

Although I have no math credentials other than a few high school courses (so far), I would think that 0 * infinity = 0 because it would mean infinity zero times, which is 0 (because anything zero times is zero)...or you could think of it as an infinite number of 0's, which is still just 0...Sorry if this wasn't worth reading...

or you could say, zero infinity times, which could be anything. You need to get a better comprehention of infinity and know that it is FOREVER.

0 × infinity is indeterminate. It could be anything.

0 × infinity = 42 is as good an answer as any.

To make the question meaningful, you really need to introduce a rigorous process involving the limit of one or more functions.

0 x infinity IS 0 summed over infinity however which should never lead to 42 right?! :confused:

I'm still not understanding why 0 x infinity could be any number....Its infinity ZERO TIMES OVER, which equals ZERO no matter what...I mean, just by using a basic property you learn in junior high school, 0 x [absolutely anything] will equal 0 because its that value ZERO TIMES OVER...Sorry if I'm being annoying about this, but the answer seems realllly obvious to me...I must be overlooking something...

I'm still not understanding why 0 x infinity could be any number....Its infinity ZERO TIMES OVER, which equals ZERO no matter what...I mean, just by using a basic property you learn in junior high school, 0 x [absolutely anything] will equal 0 because its that value ZERO TIMES OVER...Sorry if I'm being annoying about this, but the answer seems realllly obvious to me...I must be overlooking something...

Yes you are looking over something.... usally people jump to the conclusion that 0*inf = 0 , mainly because they forget infinity isn't a real number, it is forever.

Yes 0 times any real number is 0, but infinity isn't a certain number.

EDIT: Sorry, I just read in the other thread about infinity and zero...James R says that different rules apply to infinity because its not an actual number, rather, its a concept...Sorry for the confusion :-P

Here's something to think about...
How long is a point? How many points are there in a 42cm line segment? how long are all those points put together?

The fact that zero x infinity has not been discerned by mathematics or mathematicians means that mathematics is a failing if not failed discipline. The basis of mathematics is unestablished when it is gone into in depth. Without wanting to be mundane or controversial, solid geometry is by far a superior logic to a discipline that can't claim foundation.

good night fair world. May tomorrow bring logic.

leeaus

EDIT: Sorry, I just read in the other thread about infinity and zero...James R says that different rules apply to infinity because its not an actual number, rather, its a concept...Sorry for the confusion :-P

Even though its not a real number (I can understand that it is a concept) that doesn't explain why 0 x infinity (which is 0 summed over infinity) should lead to 42! Take this:

0 x 10 = 0
0 x 1000 = 0
0 x 1000000 = 0
0 x 1000000000 = 0
0 x 1000000000000 = 0
0 x 1000000000000000 = 0
0 x 1000000000000000000 = 0
0 x 1000000000000000000000 = 0
0 x 1000000000000000000000000 = 0
.....
.....
0 x <FONT FACE="Symbol">¥</FONT> = 0

Where does this rule break down. The limit of 0 x y as y approaches infinity is zero!

Hello Jc.
0 makes infinity absent? Look at the second last line of your post. You allow a predominance to one of two indeterminants.

regards leeaus

Where does this rule break down. The limit of 0 x y as y approaches infinity is zero!

Look at the limit of x * y as x approaches 0 and y approaches &infin;. Depending on how they approach 0 and infinity respectively affects the limit of their product.

For example if x heads along the sequence 42, 42/10, 42/100, 42/1000,...
and y heads along 1, 10, 100, 1000,... their product looks like:

42 * 1 = 42
42/10 * 10 = 42
42/100 * 100 = 42
42/1000 * 1000 =42
...

By this choice of sequences it would seem fair to conclude 0 * &infin; = 42. But by choosing different sequences, you can actually get any result you like. You might think that allowing both x and y to vary is unfair, but this is exacly what will make the operation jibe with limits. Try to come up with two sequences approaching 2 * 3 where the product of these sequences approaches something other than 6. You can't. For multiplication you only run into this problem with 0 * &infin;, which is why you'll hear people call it an indeterminate.

don't understand the 42 deal...

why 42 and not 152? or any other real number?

on the other hand

Infinity / 1 = Infinity
Infinity / 10 = Infinity
Infinity / 100 = Infinity
Infinity / 1000 = Infinity
Infinity / 10000 = Infinity
Infinity / 100000 = Infinity
Infinity / 1000000 = Infinity
Infinity / 10000000 = Infinity
Infinity / 100000000 = Infinity
Infinity / 1000000000 = Infinity
Infinity / 10000000000 = Infinity
Infinity / 100000000000 = Infinity


it's exactly the same thing

when you are dealing with uncertains
the result is indertemined
therefore

0 x Infinity is neither 0 or infinity and neither 42 or 152 or 13872847

it's simply indertermined

it can be any number or no number at all

a expression like that doen't have a meaning to exist

when you divide 25 by 3 you want to "know" something

for instance the old pie division

you have 25 pies and want to give them to 3 persons

that's the purpose of a division

or an addition

20 dolares multiplied by 25 pies....you want to know how much will you win in dolares


but now...what's the purpose of dealing with 0's and infinitys?

0 (that means nothing...the absence of something)
and...
infinity (that means everything...a "number" beyond all numbers..something that goes beyond every single quark that exists in this universe...something that is simply unreachable)

what's the purpose of dealing with this kind of things?

we use math is to solve possible and reachable problems and questions

and until now it hasn't failed us

math always had given us the right answer

there might be a day when we find out that math is another wrong approach in the understanding of the universe
but until now it's our best alied in the quest for the truth

and infinity's and 0's are exactly what math cannot be

infinity doesn't exist...
for instance when you say the universe is infinite you are saying that beyond the furthest galaxy...beyond the furthest light or energy there "are" and infinity of nothing....existence is finite

there are a finite number of matter and energy (E=MC2)

what is infinite is then the nothingness


but that is a paradox an infinity of nothing?

does that make sense?

nothing is nothing....

end...over....the absence of everything

and that's what some people cannot understand

what exists is finite

what doesn't exist is infinite


0 = infinity

can someone deny it?

Nice sequence Shmoe! I think I understand now :)