Basic question about BJT
There are many, many questions about ground on this website so I will be brief: Voltage is always measured between two points in a circuit. Ground, or 0, in a circuit like this is precisely where you want it to be - usually where it makes sense. Let's redraw your circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Does that make more sense? You can only pick one node in this circuit to be your ground, but you can pick any node. I have drawn it so that the emitter node would be the most reasonable place, because then the other nodes will be positive in reference to that point.

As you can now see, it is now quite clear that the base and the emitter is at different potentials.

A lot of confusion comes from a lousy schematic layout. Sometimes it is because the lecturer has limited experience actually designing real world circuits, but in this case I think it's deliberate - they want you to think about the current flow, and the relative voltages between every node. Mission accomplished. They got you confused, you started to think, and hopefully your first thought next time you find something like this is to redraw it so that it's sane: more positive nodes on top, inputs to the left, outputs to the right, current flows from top to bottom and left to right.