You have a point in space. You can go one Planck length to the right - that's the minimum length allowable. You can go one Planck length straight up at right angles to our first point - that's the minimum length allowable. But (via Pythagoras) the length between the two ends of our constructed triangle (in real space remember) is root 2: an irrational number! How is that possible? As that is not possible the idea that there is a minimum length (Planck or other) is false. Q.E.D.
Don't take my musings seriously. I'm just having fun. But I did wonder about this "argument". You might say there are already plenty of triangles written on blackboards with sides 1 inch/1 inch/ root 2 inches. Well yes, but the inch is just a conventional length. So irrational lengths in inches are just "notional". But the Planck length sounds like an absolute length; so we get an "absolute" real-world irrational length! Sounds dodgy to me. Pity about this Planck length boundary. I was hoping there'd be many tiny worlds with tiny people having their own adventures . . . https://www.youtube.com/watch?v=lgZQ8gyUlwI https://www.youtube.com/watch?v=lgZQ8gyUlwI
