What number set is Q (rational) with a line over it?

Jan 2009
14
0
I have a question asking if an irrational number belongs to the number set:
_
Q

Q normally means rational, but what does that line mean? I assume the irrational number still wouldn't be included in that set?
 

mathman

Forum Staff
May 2007
6,932
774
Usually a line over a symbol for a set means the complement of the set. In this case the complement of Q is the set of all irrationals (assuming the whole space referred to is the reals).
 
May 2008
1,300
0
York, UK
It could also mean the closure of the set, in which case (considering it as a subset of the reals, and in the usual topology on \(\displaystyle \mathbb{R}\)) we would have \(\displaystyle \bar{\mathbb{Q}}=\mathbb{R}.\)