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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

1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001