Is this backslash a typo here in showing a function?

Question

"Then there exists a homogeneous function $\rho\in C^\infty(R^n \backslash\{0\},R^n)$ with negative degree of homogeneity which specifies the following properties:" - Pablo Monzon (2006), Almost global stability of dynamical systems, page 27., Link to the e-book

Does backslash have a meaning in this context in math. According to Wolfram Mathworld it can sometimes have meaning. But, does it have one here?

user190080 · Accepted Answer · 2015-09-15T14:10:39.960

5

Yes, it has a common meaning. In general for two sets $A$ and $B$, $$ A\backslash B \equiv A\text{ without } B $$ so in your case, $\mathbb{R}^n\backslash\{0\}$ means $\mathbb{R}^n$ without the origin $0$ or $$ \mathbb{R}^n\backslash\{0\}\equiv\{x\in\mathbb{R}^n:||x||>0\} $$ As Daan Michiels points out, the notation of set difference does sometimes vary, for example $$ \mathbb{R}^n - \{0\}\equiv\mathbb{R}^n\backslash\{0\} $$ is also used to express this. You might also have a look here.

edited Sep 15 '15 at 14:10

answered Sep 15 '15 at 14:04

user190080

3,701

1

https://en.wikipedia.org/wiki/Complement_(set_theory)#Relative_complement It is sometimes written as $\mathbb{R}^n - {0}$. – Daan Michiels Sep 15 '15 at 14:05
@DaanMichiels that's true (+1 for your answer), but I know it mostly in the form of $A\backslash B$ – user190080 Sep 15 '15 at 14:06
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Yes, I also use the backslash, but I often see the minus-sign. The TeX command for the backslash is actually explicitly called \setminus, so it seems like a good choice. – Daan Michiels Sep 15 '15 at 14:09
@DaanMichiels updated the answer! I didn't know that there was an explicit $\TeX$ command for this, thanks for this info! – user190080 Sep 15 '15 at 14:12
Yes, \setminus was a good tip actually! – Mehdi Haghgoo Sep 15 '15 at 14:53

Is this backslash a typo here in showing a function?

1 Answers1