Algebra
Floor and Ceiling Functions
What is \(\left\lfloor\sqrt{46}\right\rfloor?\)
Which of the following statements is/are true?
I. \(\lfloor x+n\rfloor=\lfloor x\rfloor+n\) for any real \(x\) and any integer \(n.\)
II. \(\lfloor x\rfloor+\lfloor-x\rfloor=0\) if and only if \(x\) is an integer.
III. \(\lfloor x\rfloor+\lfloor y\rfloor\le\lfloor x+y\rfloor\le\lfloor x\rfloor+\lfloor y\rfloor+1\) for any real \(x\) and \(y.\)
What is the solution set to \(\left\lfloor \frac{x}{2}\right\rfloor=4?\)
How many integers \(x\) satisfy the equation \[\lfloor\sqrt{x}\rfloor=3?\]
What is \(\lfloor \pi \rfloor?\)