# Inspired by 'Floor Ceiling Ceiling Floor : JEE Style'

Algebra Level 4

$\large \displaystyle (\lceil x + 1 \rceil)^2 + (\lfloor x -1 \rfloor)^2 = (\lceil x -1 \rceil)^2 + (\lfloor x + 1 \rfloor)^2$

The solution set of the equation above is?

Notations:

$$\mathbb{R}$$ denote the set of real numbers.

$$\mathbb{Z}$$ denote the set of integers.

$$\mathbb{N}$$ denote the set of natural numbers.

$$\mathbb{Q}$$ denote the set of rational numbers.

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