Dude, we've been over this many times--nothing in the physical world has infinite resolution. No analog amplifier has ever had infinite resolution.
Why don't you use that scope of yours to measure the bandwidth of, say, the 12AX7 stage in a tube amp? Is it in the terahertz range? Gigahertz? Well? How infinite is it? I'll give you a hint and tell you it partially depends on the circuit gain and source impedance of your test signal because of Miller capacitance, but the tube has its own limit as well.
Can you accept that as a law of physics that no amplifier has infinite bandwidth, which is required for infinite resolution?
Can you further accept that because of thermal noise (that pesky Johnson again) that infinite dynamic range is impossible because you cannot cool a circuit to absolute zero? And even if you did get cold enough to make a difference in thermal noise, you'd still have noise in the active components of your circuit?
So we can clearly understand that no analog circuit--never mind a recording, I am just talking about amplifiers--can come remotely close to infinite resolution. Jim Williams tries pretty hard; he uses just about the fastest and lowest noise audio circuits of anybody I know of. Don't ask him what he thinks about tape though . . . but I think he claims his circuits at about 150dB dynamic range and 200kHz bandwidth at 80dB gain or so. Impressive, but not infinite.
Next, let's get back to talking about how the bias signal in a tape recorder serves as a bandwidth limit--actually half the bandwidth of the bias frequency, otherwise you would get intermodulation distortion into the audio bandwidth.
You were going to measure that, remember?