Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In a book I see the following

" The concept of the winding number s usefull to characterize what is meant by the inside(interior) and the outside(exterior) of a closed curve $\gamma$, respectively, in the following way $$Int(\gamma)=\{z\notin\gamma:n(\gamma;z)\neq 0\}$$ and $$Ext(\gamma)=\{z\notin\gamma:n(\gamma;z)=0\}$$ Moreover, a closed curve $\gamma:[a,b]\rightarrow\mathbb{C}$ is said to be positively oriented if $n(\gamma;z)>0$ for every $z$ inside $\gamma$ and negatively oriented if $n(\gamma;z)<0$ for every $z$ outside $\gamma$"

my question is: "negatively oriented if $n(\gamma;z)<0$ for every $z$ outside $\gamma$" makes no sense to me as the author already defines $Ext(\gamma)=\{z\notin\gamma:n(\gamma;z)=0\}$, I mean when $z$ is outside gamma by definition $n(\gamma;z)=0$, I am confused please teach me.

share|improve this question
2  
I think it is a typo. Replace outside by inside and you'll be fine. –  Gregor Bruns Aug 25 '12 at 21:34
    
Yes, it sounds like a slip-of-tongue (finger?) to me. –  anon Aug 25 '12 at 21:38

1 Answer 1

You're right, this is a typo. See wolfram's definition (two images with values $\pm 1$), it is very clear that $z\in Int(\gamma)$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.