# 1/oo = 0 ?

1. Aug 7, 2007

### Nick666

Well? Is it equal to zero ? If there are threads with this subject, redirect me to them please.

2. Aug 7, 2007

### Kummer

Please look in the philosophy forum.
(Because this is not a topic mathematicians discuss, just philosophers.)

Last edited: Aug 7, 2007
3. Aug 7, 2007

### mgb_phys

To an engineer or physicist yes.
We aren't as squeamish as mathematicians when it comes to needing an answer.

4. Aug 7, 2007

5. Aug 7, 2007

### homology

Or, heck, check out nonstandard analysis... But I assume you're (Nick666) talking about calculus and perhaps a limit that comes up? The idea is that 1/big is small, and 1/bigger is smaller, and so I can always choose an x to make 1/x as small as you'd like it (or as close to zero).

Cheers,

Kevin

6. Aug 7, 2007

### Moridin

Here is the correct mathematical notation:

$$\lim_{x\to\infty} \frac{1}{x} = 0$$

1 over infinity is not a valid computation. Actually, it should be that "the limit of 1 over x as x goes to infinity is equal to zero".

7. Aug 7, 2007

### matt grime

Oh dear, so many misconceptions here.

1/oo is a perfectly good symbol. In the extended complex plane it is 0. As it would be in the extended reals - you do not need limits at all to answer that. However, the symbol 1/oo does not have a canonical meaning - I can think of no symbol in mathematics that has a canonical meaning. It's not even true that there is a unique meaning for the symbol 1, or 0 for that matter, is there, so why should there be such a meaning here?

8. Aug 8, 2007

### jostpuur

Nick666, do you know yourself what you mean with the infinity? Is there a definition you are using?

9. Aug 8, 2007

### Nick666

Let oo be 999... :) . ( oh, can 999... be infinity ?)

Last edited: Aug 8, 2007
10. Aug 8, 2007

### HallsofIvy

Staff Emeritus
Now you're just pulling our chain!

11. Aug 8, 2007

### jostpuur

If you write 999..., I'm afraid I'll have to ask again, that do you know yourself what you mean by that?

For example, a number 123 is $1\cdot 10^2 + 2\cdot 10^1 + 3\cdot 10^0$. In general natural numbers can be written as $\sum_{k=0}^N a_k 10^k$, where for all k $a_k\in\{0,1,2,\ldots,9\}$. Your number starts like $9\cdot 10^{?} + \cdots$, and what do you have up there in the exponent?

Writing ...999 would make more sense, because it would be $\sum_{k=0}^{\infty} 9\cdot 10^k$, but I don't know what this means either, because the sum doesn't converge towards any natural number.

It seems your problem is, that you don't know what you mean with the infinity. If you are interested in the basics of analysis, I think Moridin's answer has the point. $\infty$ is a symbol, that usually means that there is some kind of limiting process. The symbol doesn't have an independent meaning there, but it gets meaning in expressions like $\lim_{n\to\infty}$ and $\sum_{k=0}^{\infty}$.

12. Aug 8, 2007

### Nick666

999... As in infinitely many 9`s .

And 1/"that sum you wrote" = ?

13. Aug 8, 2007

### Nick666

And another question about the sum you wrote. Isnt every element of that sum a natural number? (9, 90, 900, 9000 etc) Or let me put it another way. 10^k, when k ->oo , isnt that a natural number ? I mean, if we multiply 10 by 10 by 10........ and so on, shouldnt we get a natural number?

Last edited: Aug 8, 2007
14. Aug 8, 2007

### CompuChip

Yes it is.
So is every partial sum (cutting off the summation after a finite number of terms).
But the sum itself isn't.

15. Aug 8, 2007

### Nick666

See my above edited post.

But if we add a bunch of natural numbers, no matter how many, isnt it logic that we should also get a natural number ? (or maybe this is why I got low grades at math haha)

16. Aug 8, 2007

### jostpuur

No at all! $\lim_{k\to\infty} 10^k$ is not a natural number.

17. Aug 8, 2007

### Moridin

As you cannot compute [itex]\infty[/tex] (division by zero is undefined), how would it be possible to compute something that involves it without using limits? I'm not sure I understand.

18. Aug 8, 2007

### matt grime

It's just a symbol. One that is used in the context of limits in analysis, and one that is not "computed' (whatever that means) in terms of limits in other contexts.

19. Aug 8, 2007

### Moridin

20. Aug 8, 2007

### Nick666

I still dont understand how, if you add a natural number to a natural number and another natural number and so on,you dont get a natural number. If you add 1 apple and 1 apple and 1 apple and so on, dont you get an infinite number.... of apples ???