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Solve this inequality

  1. Apr 22, 2013 #1


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    1. The problem statement, all variables and given/known data
    [itex]x^2 \geq [x]^2[/itex]

    [] denotes Greatest Integer Function
    {} denotes Fractional Part
    2. Relevant equations

    3. The attempt at a solution

    [itex] x^2-[x]^2 \geq 0 \\
    (x+[x])(x-[x]) \geq 0 \\
    -[x] \leq x \leq [x] \\
    Considering left inequality
    x \geq -[x] \\
    \left\{x\right\} \geq -2[x]
  2. jcsd
  3. Apr 22, 2013 #2


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    How do you go from the above step to the next step.

    (It does look valid, but an explanation seems to be in order.)

  4. Apr 23, 2013 #3


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    Ah! I made a silly mistake there. Actually it should be like this

    [itex]x \in \left( -∞, -[x] \right] U \left[ [x],∞ \right) [/itex]
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