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

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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