Left Operation is Idempotent
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Theorem
The left operation is idempotent:
- $\forall x: x \leftarrow x = x$
Proof
Immediate from the definition of the left operation.
$\blacksquare$
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Exercise $2.17 \ \text{(a)}$