Suppose that and are non-empty subsets of Define the distance between and by the formula:

1) Explain why this infimum always exists

So because,

there must be a greatest lower bound

2) Suppose that . Find

Just from drawing a picture, I see that the smallest distance between the points on the graph is 2.

Now, I'll try to plug in different values of y, and so the infimum of this is

When

3) Find 2 disjoint sets and such that

Is there any sets at all?

Not too sure if I did it correct?

Yeah I'm just edited my post to show what I've done