[talanum1 (OP)]

We have that whatever allows us to count time comes in quanta, since: say you can count as fast as you can write down successive numbers. Then if the quanta were infinitesimal we can never count further than zero since it takes an infinite time to write the number next to zero. Since we can count past zero, time must come in finite chunks or quanta.

Similarly, the proof that movement is impossible follows from assuming space is continuous.