A very good ENGINEERING explanation of why analog can not be as good as digital..

kijanki

This theorem only states that you can recover continuous signal by sampling at least two times per period. It does not say you can do that when waveform constantly changes

Actually, that’s exactly what the Fourier Transform addresses and proves - the transient need only to fall within the bandwidth of the system. It’s why digital audio works.

Again, I’m very much an analog guy. But to claim the digital audio isn’t continuous like analog is misunderstanding how digital audio works. It has problems, but non-existent stairsteps aren’t part of them.

..the transient need only to fall within the bandwidth of the system. It’s why digital audio works.

For any signal to be perfectly band limited it would have to extend infinitely in time.  There are many other shortcomings like less than perfect brickwall filters with uneven group delays, jitter in A/D or D/A conversion etc. 

kijank

For any signal to be perfectly band limited it would have to extend infinitely in time.

I’m not sure what this means, but nothing is perfect.

There are many other shortcomings like less than perfect brickwall filters with uneven group delays, jitter in A/D or D/A conversion

Agreed, of course. Digital audio is not perfect. However, the notion that it is not continuous, and is comprised of "stair-step" signals, is a misnomer. It is a false claim and that can be proven visually, as in the video that I linked, as well as mathematically.

I'm not sure what this means, but nothing is perfect.

That's all I'm saying.  

"So if they prefer lps made from corrupt digital discontnous sampled waveforms, that preference must be based upon something completely unrelated to that waveform."

The cutting head stylus cannot magically appear at the extreme displacement in one direction, disappear, and then reappear at the other extreme; it had to physically travel from point A to point B and at every physical point in between. This is why, even fed an analog signal from a digital filter, vinyl has to sound "like analog." The same goes for the playback stylus and the magnets/coils in the cartridge. The same holds true for the motion of speaker cones and your ear drums.