Can a group have repeating elements?

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A group, G, cannot have repeating elements as it is defined as a set, where each element is unique. The cardinality of a set is determined by the number of distinct elements, meaning that duplicates are not counted. Therefore, the order of G does not include repeated elements, as they do not contribute to the set's definition.

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Can a group, G, have repeating elements? And if so does the order of G include these repeated elements?

Thanks!
 
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blahblah8724 said:
Can a group, G, have repeating elements? And if so does the order of G include these repeated elements?

Thanks!

You should define what you mean by "repeating elements".

Among other things, a group is a set. When you consider the cardinality of a set that is given by a list of things, you don't count the same thing as being more than one element when it appears more than once in the list. Is that what you're asking?
 

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