# Just want to clear this up

1. Apr 30, 2004

### Warr

Is $$\frac {1}{\infty} = 0$$ , or is it just infinitely close to 0?

Last edited: Apr 30, 2004
2. Apr 30, 2004

### mathman

= is correct, the other alternative is not too meaningful, unless you get involved with non-standard analysis.

3. Apr 30, 2004

### master_coda

Unless you're using non-standard analysis I don't think the statement $\frac{1}{\infty}=0$ is even meaningful.

4. Apr 30, 2004

### jcsd

Well, you could say 1/x -> 0 as x tends to infinity (though that obviously doesn'; mean 1/inifnity = 0 especially when infinity isn't even a number).

5. Apr 30, 2004

### Warr

Lets say there is 1 unit of something in an infinitely large area...then would you say = ? Because then that says that the unit doesn't even exist...

6. Apr 30, 2004

### jcsd

No in that situation all we would be saying is that it would be meaningless to talk about the ratio of the area to the unit area.

7. Apr 30, 2004

### Warr

No it isn't...Because that unit DOES exist. But by saying 1/inf = 0...we say it is non-existant. In the same way, human population with respect to time would be 0 if the above statement were true. This is not so...

8. Apr 30, 2004

### Hurkyl

Staff Emeritus
1/&infin; doesn't have a "standard" meaning; in some systems where infinite numbers are defined, division doesn't exist. In some others, 1/&infin; is some infinitessimal positive nonzero number. In others, 1/&infin;=0.

If you're thinking of &infin; as that "big number that sits at the positive end of the real numbers", then you probably mean to use the extended real numbers, where 1/&infin; is defined to be equal to zero.

9. Apr 30, 2004

### Integral

Staff Emeritus
In my books when infinity is defined as an extension to the Real number line, operations on infinity are also defined, included with these definitions is:

$$\frac 1 \infty = 0$$

This is a very specific definition for a very specific application ie the real numbers. If you attempt to apply this definition out of context your results may vary.

10. May 1, 2004

### JonF

I always thought it meant infinitely close to zero, and that’s why the delta at the end of an integral doesn’t yield zero results, because the delta doesn’t actually = zero, just something infinitely small.