Algebra
Floor and Ceiling Functions
\[ \large {\lfloor -3.2 \rfloor =\, ? } \]
by
Mehul Arora
Given that \(x\) is a real number but not an integer, compute \( \lfloor x \rfloor + \lfloor - x \rfloor \).
by
Rohit Udaiwal
\[\left\lfloor \left| \frac{2x-3}{4} \right| \right\rfloor = 5\]
What is the largest negative integer \(x\) that satisfies the equation above?
by
Margaret Zheng
\[\left\lfloor \frac { x }{ 1! } \right\rfloor +\left\lfloor \frac { x }{ 2! } \right\rfloor +\left\lfloor \frac { x }{ 3! } \right\rfloor =224\]
Find the integer value of \(x\) that satisfies the equation above.
Note: \(\lfloor x \rfloor\) denotes the greatest integer that is smaller than or equal to \(x\).
by
Trung Đặng Đoàn Đức
\[\Large{\lceil x^2 \rceil=\lfloor 2|x| \rfloor}\] How many integers satisfy the above equation?
by
Hjalmar Orellana Soto