Say I have a group and an unknown binary operation , and . ( being the identity element)

Is it true that the only value can be is the identity element, ?

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- September 27th 2011, 06:44 PMtangibleLimeQuick question about identity element
Say I have a group and an unknown binary operation , and . ( being the identity element)

Is it true that the only value can be is the identity element, ? - September 27th 2011, 06:52 PMFernandoRevillaRe: Quick question about identity element
- September 27th 2011, 06:55 PMtangibleLimeRe: Quick question about identity element
Ah, didn't consider that. Thanks for the response!

- September 27th 2011, 09:01 PMDevenoRe: Quick question about identity element
what you can say, if a*a = e,and a is NOT the identity, is that a is of order 2, and that a is its own inverse (showing that elements of order 2 and of order 1(the identity is the only element of order 1) share this property).

a good example of an element of order 2 is the following group, which is a subset of the actions you can perform on a light switch:

{flip the switch, do nothing} and the group operation is: first do one thing, then the other.

"flip the switch" is an element of order 2: flip the switch, then flip the switch = do nothing.

(to be honest, this is in all actuality just Z2 in disguise, and is one of the basic ways in which logical circuits can "do math"). - September 28th 2011, 03:20 AMSwlabrRe: Quick question about identity element
What is true, however, is that if then is the identity. This is true because,