Idempotent Element/Examples/One is Idempotent for Multiplication
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Example of Idempotent Element
$1$ is idempotent under the operation of multiplication in the set of real numbers $\R$.
Proof
From Non-Zero Real Numbers under Multiplication form Abelian Group, $\struct {\R_{\ne 0}, \times}$ forms an abelian group whose identity element is $1$.
The result follows from Identity Element is Idempotent.
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): idempotent
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): idempotent