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blahblah8724
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Can a group, G, have repeating elements? And if so does the order of G include these repeated elements?
Thanks!
Thanks!
blahblah8724 said:Can a group, G, have repeating elements? And if so does the order of G include these repeated elements?
Thanks!
Yes, a group can have repeating elements. In mathematics, a group is defined as a set of elements with a binary operation that satisfies certain properties. This means that the same element can appear multiple times in a group, as long as it follows the group's defined operation.
A set is a collection of distinct elements, meaning each element can only appear once. In contrast, a group can have repeating elements and is defined by a specific operation that combines these elements.
No, there are no restrictions on the number of repeating elements in a group. As long as the group's operation is satisfied, any number of repeating elements can be present in the group.
Yes, a group can have repeating elements even if the operation is addition. For example, the group of integers under addition includes repeating elements such as 1+1=2 and -2+(-2)=-4.
Repeating elements do not affect the identity and inverse elements in a group. The identity element remains the same, and the inverse of a repeating element is still the same element. For example, in the group of integers under addition, the identity element is 0 and the inverse of 2 is still -2, even though 2 appears multiple times in the group.