計算機數學

(4分) How many of the following statements are TRUE? (Note: $\mathbb{Z}$ is the set of integers, $\mathbb{R}$ is the set of real numbers, and $\mathbb{N} = \{1,2,3,\dots\}$)

• $f: \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$, defined by $f(m,n) = 2m+3n$, is onto (surjective).
• $f: \mathbb{R} \to \mathbb{R}$, defined by $f(x) = x^3+x$, is one-to-one (injective).
• $f: \mathbb{Z} \to \mathbb{Z}$, defined by $f(n) = \lfloor n/2 \rfloor$, is one-to-one.
• $f: \mathbb{R}^2 \to \mathbb{R}^2$, defined by $f(x,y) = (x+y, x+y)$, is bijective.
• $f: \mathbb{N} \to \mathbb{N} \times \mathbb{N}$, defined by $f(n) = (n, n+1)$, is onto.