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Math Help - Ceiling and Floor

  1. #1
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    Ceiling and Floor

    \displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1

    Let \displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1

    \displaystyle\left\lceil x'+d\right\rceil =x'+1

    How can I translate this into the RHS now?
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    \displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1
    Of course that is not true if x\in \mathbb{Z}.

    It is only true if x\notin \mathbb{Z}.
    In which case it is well known that \displaystyle\left\lceil x\right\rceil-\left\lfloor x\right\rfloor =1
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Let \displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1
    This line should let you know x isn't an integer.
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    This line should let you know x isn't an integer.
    No should not!
    That line contains the word 'let'. Which is not part of the statement.
    You should correctly state what you mean to begin with.
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  5. #5
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    I am absolutely content with you having others help if you are going to be so touchy and not aid in the question posed. You aren't obligated to help me. I am sure others need you.

    Just to be clear by the term "you having others help" I by no means am imply for you to ask others. What I was trying to say in a nice manner was others can help me and I will be ok with it.
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  6. #6
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    Quote Originally Posted by dwsmith View Post
    \displaystyle\left\lceil x\right\rceil=\left\lfloor x\right\rfloor +1

    Let \displaystyle x=x'+d \ \ni \ x'\in\mathbb{Z} \ \mbox{and} \ 0<d<1

    \displaystyle\left\lceil x'+d\right\rceil =x'+1

    How can I translate this into the RHS now?
    I don't know what you're trying to ask.

    What are you trying to translate into what?
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  7. #7
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    I now have \displaystyle \left\lceil x\right\rceil = \left\lceil x'+d\right\rceil=x'+1

    How can I make that the RHS now?
    Last edited by dwsmith; November 14th 2010 at 05:20 PM.
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  8. #8
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    As in your other post, what is \lfloor x\rfloor+1? It is \lfloor x\rfloor+1=\lfloor x'+d\rfloor +1=x'+1.
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  9. #9
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    Quote Originally Posted by roninpro View Post
    As in your other post, what is \lfloor x\rfloor+1? It is \lfloor x\rfloor+1=\lfloor x'+d\rfloor +1=x'+1.
    Huh?

    Never mind figure it out.
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