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Math Help - [SOLVED] Transitive

  1. #1
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    [SOLVED] Transitive

    \forall a,b,c\in\mathbb{Z} a\sim b iif. \left\vert a-b \right\vert\leq 3

    Not sure how to show this. I know a\sim b, b\sim c, then a\sim c
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by dwsmith View Post
    \forall a,b,c\in\mathbb{Z} a\sim b iif. \left\vert a-b \right\vert\leq 3

    Not sure how to show this. I know a\sim b, b\sim c, then a\sim c
    it is not transitive

    \mid 5 - 3 \mid \leq 3

    \mid 7-5 \mid \leq 3

    but

     \mid 7 - 3 \mid = 4 > 3

    counter example
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  3. #3
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    Hello, dwsmith!

    If I read the problem correctly, the relation is not transitive.


    \forall\: a,b,c\in\mathbb{Z}:\; a\sim b \:\text{ iff }|a-b| \:\leq\:3

    Not sure how to show this. I know a\sim b, b\sim c, then a\sim c

    a\sim b\,\text{ means: }\,a\text{ and }b\text{ are within 3 units of each other.}

    b\sim c\,\text{ means: }\,b\text{ and }c\text{ are within 3 units of each other.}


    \text{But this does }not\text{ imply }\,a\sim c,
    . . \text{ that }a\text{ and }c\text{ are within 3 units of each other.}

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