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    5. Subtraction $a - b$ on $\reals$

    Subtraction $a - b$ on $\reals$

    Example · Elementary

    Terms

    TermThis exampleWhy
    associative ✗ Subtraction on $\reals$ is not associative, because $(5 - 3) - 1 = 1$, but $5 - (3 - 1) = 3$.
    commutative ✗ Subtraction on $\reals$ is not commutative, because $5 - 3 = 2$, but $3 - 5 = -2$.

    Distinctions using this example

    • Associative vs. commutative

    All examples · All distinctions · All definitions

    Collection: Examples

    Updated: November 9, 2026

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