For α ∈ R, let [α] denote the greatest integer smaller than or equal to α. Define d : R x
R → [0, ∞] by d (x, y) = \(\lfloor |x - y|\rfloor\), x, y ∈ \(\mathbb R\), Then which of the following are true?
1
d(x, y) = 0 if and only if x = y, x, y ∈ \(\mathbb R\)
2
d(x, y) = d(y, x), x, y ∈ \(\mathbb R\)
3
d(x, y) ≤ d(x, z) + d(z, y), x, y, z ∈ \(\mathbb R\)
4
d is not a metric on \(\mathbb R\)