I am studying Group, and have a doubt about closure:
- Closure: If A and B are two elements in G, then the product AB is also in G.
I am not a nitpicker, and just want to make sure whether A and B can be the same element?
A question about closure in group definition
3
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abstract-algebra
group-theory
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3Yes, they can, but standard notation in Group Theory is to use lower case for elements, upper case for the group and any subsets. – 2017-02-11
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2Yes, in fact if $G = \{1\}$ (a trivial group) $A$ and $B$ *have* to be the same element. – 2017-02-11
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9In fact, throughout mathematics, two distinct symbols $a,b$ are allowed to represent the same object, unless either (1) it's explicitly specified that $a,b$ are distinct objects, or (2) the context makes it clear that the objects must be distinct. – 2017-02-11