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mathmath333

  • one year ago

greatest integer function

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \lfloor{x\rfloor}= \text{greatest integer less than or equal to x} \hspace{.33em}\\~\\ & \normalsize \lceil{x\rceil}=\text{smallest integer greater than or equal to x} \hspace{.33em}\\~\\ & \normalsize \text{If }\ x\ \text{is not an integer. } \hspace{.33em}\\ & \normalsize \text{Prove that } \lceil{x\rceil} +\lfloor{x\rfloor}\ \text{is an odd integer } \hspace{.33em}\\~\\ \end{align}}\)

  2. ParthKohli
    • one year ago
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    If \(\lfloor x \rfloor = k\) then \(\lceil x \rceil = k + 1\). Add those and you get \(2k + 1\).

  3. amoodarya
    • one year ago
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    suppose x is not integer then\[ n \le x <n+1\\ \lfloor x \rfloor=n\\ \lceil x \rceil=n+1\\ \lfloor x \rfloor +\lceil x \rceil=n+n+1\]

  4. mathmath333
    • one year ago
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    looks great!

  5. anonymous
    • one year ago
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    where is that medal all button?

  6. mathmath333
    • one year ago
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    u r experiencing a bug i think

  7. dan815
    • one year ago
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    u will always add oddd + even so

  8. dan815
    • one year ago
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    |dw:1435254654160:dw|

  9. dan815
    • one year ago
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    not saying anything different from amoo but ya

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