Infinity & Zero: Debate Over Math Definitions

[PhysKid24]

Hi I was having a debate with some guys, and anyhow they were saying 0 divided by infinity is 0, and I said that it was undefined. Whose correct? Also, they said infinity divided by a number, say 2, is not infinity, that that is undefined, and I said the number is still infinity. I don;t know. Just wondering. Would you agree that 0 and infinity are not really numbers? thanks.

 

[Hurkyl]

In ordinary arithmetic, both 0/0 and ∞/2 are undefined. (The later because ∞ isn't a "number")
In the extended reals, 0/0 is undefined, and +∞/2 = +∞.

I don't see why you'd think 0 is not a number...

 

[PhysKid24]

How about infinity over zero? What's that equal to?

 

[Zurtex]

There questions are somewhat pointless if you don't grasp the meaning and use of infinity within maths. I'd suggest you'd try and find that out before asking random questions about the arithmetical process on an element which isn't a real number.

 

[PhysKid24]

Well, I use infinities all the time as a physicist in working equations to predict, say, things that will happen in the future and so forth, but when confronted with the question of infinity divided by 0, I would say it is undefined. As a physicist, I could also say that if the numerator goes to infinity faster than the denominator goes to zero, then yes, the answer is infinity, but anyhow, and mathematicians willing to give an answer to infinity over 0?

 

[dextercioby]

Arithmetics (with zero and infinity) is one thing and definitely not appliable in physics (we think of any infinity as a nonphysical situation),while TAKING A LIMIT is a totally different thing...

Any physicist should make this simple distinction...

Daniel.

 

[Zurtex]

In the real numbers infinity is undefined, in the real numbers a/0 is undefined (or something similar I forget the exact wording).

The real numbers is the most useful set for attaching number attributes to any given physical phenomenon. The extended reals on the other hand to the best of my knowledge are more of a mathematical thing.

In the extended real numbers you have the identity: 1/0 = +∞. Therefore +∞/0 = (+∞)1/0 = +∞(+∞) = +∞.

However this is totally meaningless in terms of physics.

 

[Hurkyl]

In the extended real numbers you have the identity: 1/0 = +∞

Actually, that one's undefined too.

Remember that the operations are extended to the points at infinity through continuity: what is 1/x as x approaches 0 from the negative side?

 

[PhysKid24]

Thanks, would u agree that 0 divided by infinity is somethign undefined as well? Thanks for all your help.

 

[Hurkyl]

In the real numbers 0 / ∞ is undefined, again, because ∞ is not a real number.
In the extended reals, 0 / +∞ = 0 = 0 / -∞

 

[PhysKid24]

Thanks, do u know where I can find such a statement on the internet?

 

[jcsd]

Try this page

 

[Zurtex]

Actually, that one's undefined too.

Remember that the operations are extended to the points at infinity through continuity: what is 1/x as x approaches 0 from the negative side?

Sorry for confusing the situation, guess I should actually go and learn the maths myself rather than work backwards from statements I've seen on this forum and remember them incorrectly.

But I still feel to the original poster that you should try and gain a better understanding of what infinity means in mathematics.