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\lceil \frac{2}{3}\rceil
The floor of a real number a is the largest integer number less than or equal to a. The floor of 3 is 3.
\lceil 0+\frac{2}{3}\rceil
Dividing 2 by 3 gives 0 and remainder 2. Rewrite \frac{2}{3} as 0+\frac{2}{3}.
1
The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 0+\frac{2}{3} is 1.