Is Using \leq for Subgroup Notation Incorrect?

[kntsy]

my lecturer use $\leq$ for subgroup.
For example
$H \leq S$ means H is a subgroup of S.
But is it a wrong use of notation as the less-than-equal sign is about number?

 

[HallsofIvy]

No, there are, after all, only a finite number of symbols and an infinite number of possible concepts in mathematics! As long as you are careful to say how you are using a symbol, you can "overload" it.

 

[arkajad]

Moreover, this is a frequent notation. See for instance this online course: http://user.math.uzh.ch/halbeisen/4students/gt.html"

Go to "Subgroups"

 

[Newtime]

Moreover, this is a frequent notation. See for instance this online course: http://user.math.uzh.ch/halbeisen/4students/gt.html"

Go to "Subgroups"

In fact, I've never seen this notation not used.

 

[arkajad]

In fact, I've never seen this notation not used.

In some books any special notation for H being a subgroup of G is carefully avoided. Words are always being used. In some other books it is written $$H\subset G$$ and you have to deduce from the context that H is a subgroup of G.