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Mathematics LibreTexts

2.3 Arithmetic of inequality

  • Page ID
    7427
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    Definition

    Let \(a, b\in \mathbb{Z}\). Then

    1. \(a< b\) provided \(b=a + k\), for some \(k \in \mathbb{Z_+}\).
    2. \(a> b\) provided \(a=b + h\), for some \(h \in \mathbb{Z_+}\).

    Let \(a, b\in \mathbb{Z}\).

    1. If \(a< b\) then \(a+c< b+c\), \( \forall c \in \mathbb{Z}\).
    2. If \(a< b\) then \(ac< bc\),\( \forall c \in \mathbb{Z_+}\).
    3. If \(a< b\) and \(c< d\) then \(a+c< b+d\).