What does this symbol even mean?

[powerovergame]

Homework Statement

Show for any metric space (S,d) and  e> 0 that N(e, S) <=  D(e, S) <= N(e/2, S)

Homework Equations

none

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!

 

[Mark44]

Homework Statement

Show for any metric space (S,d) and  e> 0 that N(e, S) <=  D(e, S) <= N(e/2, S)

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.

Homework Equations

none

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!

 

[flyingpig]

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

 

[phinds]

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

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.

 

[flyingpig]

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.

Use Chrome then?

 

[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.

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.

 

[Mark44]

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

 

[powerovergame]

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

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

 

[powerovergame]

Found the answer here:
http://math.stackexchange.com/questions/68614/why-do-these-inequalities-in-metric-spaces-hold
Wow that was just...
I would have NEVER guessed it right.

 

[flyingpig]

What was the symbol? Was it X?

 

[powerovergame]

What was the symbol? Was it X?

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

 

[flyingpig]

<=> is if and only if