Inspired by 'Floor Ceiling Ceiling Floor : JEE Style'

Algebra Level 4

(x+1)2+(x1)2=(x1)2+(x+1)2\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:

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

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

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

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

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