Two Sensors with a multiplication factor of 2.6x and 2.7x

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Now that is what I've been saying!!! I also said that it is good to include the model of camera used.

Quite the opposite, really. What bothers me is false and/or misleading information.

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For sure -- I don't think anyone has said, or implied, anything different. What "we" are saying is that, for example, a Sigma 135 / 1.8 on a J5 is, in fact, a Sigma 135 / 1.8 on a J5. It is neither a 364.5 / 1.8 nor "equivalent to" a 364 / 1.8.

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I'm not sure what you are trying to say about DOF. I am talking about accurately labeling the f-number. If we give the actual focal length, then we give the actual f-number. If we give the equivalent focal length, then we give the equivalent f-number. One would think this to be common sense, really.

If the smiley is tongue-in-cheek, that's fine. But if not, what is the mechanism by which the focal length of 600 mm, a physical aspect of the lens, changes to 1620 mm when the lens is mounted on an S1? Why not simply say that a 600 mm lens on an S1 is equivalent to a 1620 mm lens on FF? And if all you care about is field of view, then full stop right there. But if you care about aperture, then why not say that a 600 / 8 on a J1 is equivalent to a 1620 / 22 on FF? Because it sure as heck is not equivalent to a 1620 / 8 on FF!

With regards to the purpose of giving EXIF at all, I think the most useful information would be something like "Taken with the Sigma 135 / 1.8 on a Nikon J1 at 135 mm f/1.8 1/400 ISO 800". If you want, you could add the following to the EXIF: "(365 mm f/4.9 1/400 ISO 5800 FF equivalent)", but that addition certainly wouldn't be necessary.

Thanks! I think it's important that one's avatar catches one's "true self". 😬

Your aperture doesn't magically change, and neither does your focal length.

The obvious answer is "yes", Marc. Is your first language Canadian-French?

While searching for an actual µ4/3 f/0.9 lens I found this 29mm f/0.8 lens!

petapixel.com/2021/05/11/voigtlander-29mm-f-0-8-super-nokton-review-the-fastest-lens-in-the-world/

I have and use both a D500 as well as a D850. I also routinely crop shots taken with both of them. When pressed, I can figure out the equivalent focal length and then divide that by the aperture I used to determine the equivalent aperture. No one presses me though, in part because I never say or bother to figure out what the equivalents are, I'm just after the framing and DOF I have previsualized and when I'm happy with the results I sometimes share them as a photo with no further explanation offered (unless asked).

I hate the emphasis on the so-called "crop factor" in the lexicon of modern digital photography.

Especially when that factor for my DSLR is 1.7 - which it's manufacturer calls APS-C (nowhere near!).

I agree with you for once 😎
When the conversation goes around in circles, you need to know when to stop.

Tu mérites une étoile, pour avoir deviné 🎓

I don't even do frame/cropfactor math for focal-length-limited decisions; that is more useful at the wide end of the AOV range, IMO.

I find crop math to be a distraction. A longer "35mm-equivalent focal length" has no value except as a limitation. Focal-length-limited photography is best thought about, IMO, in a model of subject size and lighting, distance, and pupil size. Those are what determine the main analog qualities of the subject as projected on the sensor. The next tier of considerations is pixels-on-subject, and the usability of the angle of view, but the angle of view has nothing to do with subject quality, if it doesn't crop away any of the subject.

1) Subject size - subject distance - pupil size

2) Focal length divided by pixel pitch (preferring less aberration than necessary diffraction)

3) AOV - doesn't affect subject quality, but there may be a sweet spot for operation of the camera.