Answer by fleablood for How to prove property of greatest integer function:
If you introduced the notation {$x$} = $x - [x]$ and note $0 \le \{x\} < 1$ this becomes easy.$0 \le \{x\} + \{y\} < 2$.Case 1: $0 \le \{x\} + \{y\} < 1$.Note for integers $n, m$ and $0 \le r...
View ArticleAnswer by Caleb Stanford for How to prove property of greatest integer function:
If $n$ is an integer and $t$ any real number, then it is straightforward to show that$\lfloor t + n \rfloor = \lfloor t \rfloor + n.$Therefore, since $\lfloor x \rfloor$ is an...
View ArticleHow to prove property of greatest integer function:
How can we prove that $$\lfloor x + y \rfloor = \lfloor y + x - \lfloor x \rfloor \rfloor + \lfloor x \rfloor$$ for all real $x$, where $ \lfloor x \rfloor$ denotes greatest integer less than or equal...
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