Is Using \leq for Subgroup Notation Incorrect?

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The use of \leq to denote that H is a subgroup of S is a common practice in mathematical notation, despite its origins in numerical comparisons. While some argue that this notation is misleading because it traditionally represents less-than-or-equal relationships, it is widely accepted as long as the context is clearly defined. Alternative notations, such as H ⊆ G, are also used, but they may require contextual interpretation to indicate subgroup status. The discussion highlights that mathematical notation can be overloaded, allowing for flexibility in symbol usage. Overall, the notation \leq for subgroups is prevalent and not considered incorrect in many mathematical contexts.
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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?
 
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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.
 
Moreover, this is a frequent notation. See for instance this online course: http://user.math.uzh.ch/halbeisen/4students/gt.html"

Go to "Subgroups"
 
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arkajad said:
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.
 
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Newtime said:
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.
 

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