Confused on application of Anti-Aliasing Filter
Math and Physics are not the same thing. They can be very close but infinity is hard to realize.  Going from analog to digital, a more accurate description is an average of the waveform over a small time window and the average is in turn quantized. Filters don’t have infinite stop bands but 80 dB is usually more than good enough.  There is always a small error, but one can bound it.