"In a discrete metric space, any geodesic triangle is degenerated, so every such spaces would be hyperbolic." Is it saying that as long as the space is discrete metric space then the δ value of every triangle under the distance function is always a finite number? And δ is always very small?

Thanks for your reply! But I didn't quite understand the sentence "The geodesic triangles in non-geodesic metric spaces does not work". Could you please illustrate a little bit?