Yes, the problem was defined in such a way that there was an infinity problem. If I read your question properly, I translate it as:

let d be a finite distance and v be a finite, non-zero velocity,

d/v = ∞

solve for v.

The is no non-zero value that v can have to satisfy the equation. Infinity should usually be dealt with as a limit anyway...

Now there are a few tricky ways out of your proposed problem:

For instance, you can leave point A at any finite velocity headed away from point B, and never get there.