What does $\mathbb{R}\setminus S$ mean? I am not getting it what it actually means. I have found it manywhere in real-analysis like in the definition of boundary points of a set. Can anyone tell me what it means really?
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4Note also that it is often denoted $\mathbb{R}-S$. But $\mathbb{R}\setminus S$ is prefered in classical analysis since it is not really a "subtraction" in the sense of adding and subtracting real numbers. – Mauricio Tec May 20 '15 at 02:17
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That symbols means set difference. It is called \setminus in $\TeX.$
If $A$ and $B$ are sets, then $A \setminus B$ is the set of elements in $A$ but not in $B$.
lhf
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@Bob1123, see also http://math.stackexchange.com/questions/114488/how-to-pronounce-setminus. – lhf May 20 '15 at 02:18
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Thanks for the answer , sir. I was at a dilemma which ans to accept. But, since you have got already 4+ , I better deemed it apt enough to pick the later. Nevertheless, thanks for helping me, sir. – May 20 '15 at 02:27
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If $S$ is a set and $\Bbb R$ is the set of all real numbers then $$\Bbb R \setminus S = \{x \mid x\in \Bbb R \wedge x \not\in S\}$$ meaning it's the set of all elements $x$ such that $x$ is a real number and $x$ is not an element of the set $S$.
For instance $\Bbb R \setminus \{0\}$ is the set of all real numbers except $0$.
This operation is called relative complement or set difference.
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I know the difference between sets but didn't know about this notation. Thanks. – May 20 '15 at 02:24
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1@user36790 Also, $\mathbb{R}\setminus S=\mathbb{R}\cap S^C$, etc. If you knew to typeset $\mathbb{R}\setminus S$ using
\setminus... I'm somewhat surprised. Well, now you have several ways of looking at the notation. – Daniel W. Farlow May 20 '15 at 02:26 -
@MagicMan: It was bothering when I was not getting the required result. However, I fixed it myself! – May 20 '15 at 02:30