Question
Show that if $x$ is a real number, then $\lceil x\rceil-\lfloor x\rfloor= 1$ if $x$ is not an integer and $\lceil x\rceil-\lfloor x\rfloor= 0$ if $x$ is an integer.
Step 1
In this case, we know that there exists an integer $n$ such that $n < x < n+1$. This is because $x$ is not an integer, so it must lie strictly between two consecutive integers. Show more…
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