Is the statement true for all real numbers? Explain.

Answer:

The statement is not true for all real numbers. It is only true for noninteger (decimal or fractional) values of x. If x is an integer, the ceiling function ⌈x⌉ equals x, but the floor function ⌊x 1⌋ equals x 1. Since x does not equal x 1 for any integer, the equation does not hold when x is an integer.