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We extend this characterization in two directions.\n  First, we show that $\\FO(\\Z,+,\\leq)$-definable \\emph{functions} are exactly the piecewise linear functions (Theorem~\\ref{thm:integer}), and that $\\FO(\\R,+,\\leq)$-definable functions are also exactly the piecewise linear functions (Theorem~\\ref{thm:real}). 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