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For a real number \(x,\) find the number of different possible values of \(\lfloor x \rfloor + \lfloor -x \rfloor.\)

 May 8, 2019

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 #1
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\(x \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = 0\\ x \not \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = -1\)

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 May 8, 2019
 #1
avatar+6046 
+1
Best Answer

\(x \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = 0\\ x \not \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = -1\)

Rom May 8, 2019

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