Question 147
Let $[x]$ be the greatest integer not exceeding $x$. Consider the statements
a. $[x+y] = [x] + [y]$.
b. $[-x - y] = [-x] + [-y]$.
Characterise the pairs $x, y$ of real numbers such that at least one of (a) or (b) is true and characterise the pairs $x, y$ such that both (a) and (b) are true.
a. $[x+y] = [x] + [y]$.
b. $[-x - y] = [-x] + [-y]$.
Characterise the pairs $x, y$ of real numbers such that at least one of (a) or (b) is true and characterise the pairs $x, y$ such that both (a) and (b) are true.