# What does this symbol even mean?

1. Oct 5, 2011

### powerovergame

1. The problem statement, all variables and given/known data
Show for any metric space (S,d) and  e> 0 that N(e, S) <=  D(e, S) <= N(e/2, S)

2. Relevant equations
none

3. The attempt at a solution
Can somebody please tell me what does N(e,S) or D(e,S) even mean so I can at least know what I am asked to prove?

I dig through all the notes, and online sources and could not find anything operation that involves a metric space with a real number.

Thanks!

2. Oct 5, 2011

### Staff: Mentor

My browser (IE 8) shows empty boxes for six of the symbols above.

Do you have a textbook? If so, it should define any notation like this that is used. N(. , .) could mean "neighborhood", but the notation used in the text I studied for my Topology class uses N(p, ε) to mean the ε-neighborhood of a point p in set S.

3. Oct 5, 2011

### flyingpig

Mark...don't use Internet Explorer. This is 2011, use Mozilla FireFox.

4. Oct 5, 2011

### phinds

FireFox is pure crap for a lot of operations, so some of us shun it. For the casual user it seems OK but if you are a software developer, it is useless.

5. Oct 5, 2011

### flyingpig

Use Chrome then?

6. Oct 5, 2011

### powerovergame

Uh they are just all regular texts. Thanks for your help, I suspected it meaning neighborhood too, you see, neighborhood is defined by a point and a positive number. Here it is just a metric space and a positive number, what kind of things can be defined out of this?

And this class doesn't have a textbook. We use only a power point slide, which I look through at least 10 times and found nothing that relates to this.

It feels one way when you don't know how to prove a statement, but it feels totally different when you don't even know what statement you are asked to prove.

7. Oct 5, 2011

### Staff: Mentor

Unless someone else here can decipher this, you should ask your instructor what the notation means.

8. Oct 5, 2011

### powerovergame

If there was time I would't be here. Oh well..... it's life. It's funny how the instructor just put it there as if it a commonly used notation

9. Oct 5, 2011

### powerovergame

10. Oct 5, 2011

### flyingpig

What was the symbol? Was it X?

11. Oct 5, 2011

### powerovergame

Symbols here <==> Symbols in the link [p]
S X
d rho
N N
D M

12. Oct 5, 2011

### flyingpig

<=> is if and only if