You’re not wrong but you may be overinterpreting the significance of what you report. It is true that you can never measure something truly continuous with infinite precision. But, this isn’t that interesting because there are physical limitations on measurement that are much more relevant in any given context. The probability theory issue here (and the relevant mathematical terms if you want to follow up on this are “almost surely” and “measure zero) doesn’t say anything about measuring as precisely as you’d like; it just rules out truly infinite precision.
I’m not a physicist, so this may not be quite right, but my basic understanding is that there are inherent physical limits on measurement precision and not merely apparatus-dependent ones. That is one can’t, in principle, measure anything shorter than a Planck length, for example.
You’re not wrong but you may be overinterpreting the significance of what you report. It is true that you can never measure something truly continuous with infinite precision. But, this isn’t that interesting because there are physical limitations on measurement that are much more relevant in any given context. The probability theory issue here (and the relevant mathematical terms if you want to follow up on this are “almost surely” and “measure zero) doesn’t say anything about measuring as precisely as you’d like; it just rules out truly infinite precision.
I’m not a physicist, so this may not be quite right, but my basic understanding is that there are inherent physical limits on measurement precision and not merely apparatus-dependent ones. That is one can’t, in principle, measure anything shorter than a Planck length, for example.