33 -21 Let $[x]$ denote the greatest integer not exceeding $x$. For any real number $x$, which of the following statements is correct?
(A) $[x]=|x|$.
(B) $[x] \geqslant \sqrt{x^{2}}$.
(C) $[x]>-x$
(D) $[x]>x-1$.
(China Beijing Junior High School Mathematics Competition, 1985)
[Solution] The range of $[x]$ takes all integers. $[-2]=-2$, while $|-2|=2$, $\sqrt{(-2)^{2}}=2$. We can eliminate $(A),(B)$,
also $-(-2)=2$, so $[-2]<-(-2)$, we can eliminate $(C)$.
Therefore, the answer is $(D)$.