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Yes, idempotent is playable

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Found in the following dictionaries

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SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Idempotent" Definition

adjective

Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed. In algebra, xn = x for all positive n.
Source: Wiktionary
Relating to or being an operation under which a mathematical quantity is idempotent.
Relating to or being a mathematical quantity which when applied to itself under a given binary operation (as multiplication) equals itself.

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