◀ ▲ ▶Branches / Algebra / Proof: Zero (Absorbing, Annihilating) Element, Left Zero, Right Zero
Proof: Zero (Absorbing, Annihilating) Element, Left Zero, Right Zero
(related to Proposition: Uniqueness of the Neutral Element)
- Let $(X,\ast)$ be an algebraic structure and let $e,f$ be neutral in $X.$
- By definition of neutral, we have $f=f\ast e=e\ast f=e.$
- Therefore, $e$ is unique.
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References
Bibliography
- Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001