Prove that {$a ∈ ℤ : a ≤ k$} has a greatest element How can I prove that the set {$a ∈ ℤ : a ≤ k$}, where $k∈ℝ$, has a greatest element?
I have tried using the Well-ordering theorem in order to get a contradiction but I'm having trouble with my approach.
Thanks.

Hint: The floor function: $\lfloor k \rfloor$. For example, if $k$ were $2.1$, then the greatest element of your set would be $2$.
