1
$\begingroup$

Here's the set:

$\{x:x<8\} \setminus \{5\}$

What does the "\" operator mean?

  • 1
    It usually represents the set theoretic different http://en.wikipedia.org/wiki/Setminus#Relative_complement2011-05-04

3 Answers 3

6

See http://en.wikipedia.org/wiki/Complement_%28set_theory%29

for "relative complement", "set-theoretic difference".

6

It means that you are looking at all values less than $8$ without considering $5$. What you have written is not completely correct. If you are talking of real numbers less than $8$ and not equal to $5$ you will write it as $\{x \in \mathbb{R}:x<8 \} \backslash \{5\} = \{x \in \mathbb{R}:x<5 \} \cup \{x \in \mathbb{R}:5 or if you are talking of natural numbers less than $8$ and not equal to $5$ you will write it as $\{x \in \mathbb{N}:x<8 \} \backslash \{5\} = \{0,1,2,3,4,6,7\}$ or if you are talking of integers less than $8$ and not equal to $5$ you will write it as $\{x \in \mathbb{Z}:x<8 \} \backslash \{5\} = \{x \in \mathbb{Z}:x<5 \} \cup \{6,7\}$ It is incorrect to write $\{x:x<8 \} \backslash \{5\}$ without specifying where $x$ belongs

In general, $A \backslash B = A \cap B^c$

  • 0
    Thanks for the detailed explanation. Unfortunately, user9325 got there first.2011-05-04
1

Intuitively similar (but not really) to minus. So if $A=\{1,2,4\}$ and $B=A\setminus\{2\}$, then $B=\{1,4\}$.

in your case, the set is $\{x:x<8, x\neq5\}$.

Look at the other answers wiki link.