Left and right identities of associative operations are the same ↩

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created: 2022-11-12 02:13:30
modified: 2022-11-12 02:20:21

Statement: If a binary operation

is associative¹ and if

is a left identity and

is a right identity, which means that:

and

then:

Proof

From each of the definitions of and , we get the following:

and

But then they must equal:

QED