But that's the step at which information is lost, but you're part of the process.

Wrong! No information is lost at that point, because you cannot loose what you never had. Agreed, the image as captured by the camera does not contain all the data available at the original scene, but then neither do your eyes!

They omit capturing the infra-red part of the spectrum & below; and the ultra-violet spectrum & above. Come to that, the camera does not capture the temperature, or your personal mood. All of which is totally irrelevant.

The TIFF format failthfully records, in a lossless manner, all of the information available at the point of capture. Anything else, including the size of your hat is information available at the original scene, but not lost, because it was never captured.

For you to have a PNG of a certain file size, you are picking an upper-bounded width and height to take your picture.

This is also irrelevant. You don't start with a file size and then say "How big an image can I fit in it". You start with an image of a given size (width x height x color depth) and say how big will the file be when I save this to disc.

• Tiff record everything available at the point of capture. That is, the digitally encoded recording of the result of analog-to-digital conversion performed at the point of capture.
• PNG will use LOSSLESS compression techniques to reduce the filesize without throwng away information available in that original image.
• JPG will also use compression techniques reduce the filesize, and can reduce the filesize more than PNG. However, regardless of the options chosen, even if you specify minimum compression, JPG will still discard what it chooses to deem irrelevant detail from the original image.

This is the reason the 'ISO SC29/WG1' committee, otherwise known as the Joint Photographic Experts Group defines the JPEG image compression standard as

JPEG is "lossy," meaning that the decompressed image isn't quite the same as the one you started with. (There are lossless image compression algorithms, but JPEG achieves much greater compression than is possible with lossless methods.) JPEG is designed to exploit known limitations of the human eye, notably the fact that small color changes are perceived less accurately than small changes in brightness. Thus, JPEG is intended for compressing images that will be looked at by humans. If you plan to machine-analyze your images, the small errors introduced by JPEG may be a problem for you, even if they are invisible to the eye.

JPEG allows you to make that tradeoff later in the cycle by trading some of the individual bit accuracy for the overall pixel count.

So wrong! The implication of that statement is that JPEG can somehow increase the size of the image provided you accept that color of the individual pixels may not be the same as they started out. JPEG can't autovivify extra pixels for you. It can only throw away detail from the original captured image--which further reduces the fidelity from the original scene--in order to save a few bytes of disc-space or bps of bandwidth. The information lost is carefully chosen, and if disc-space or bandwidth are your criteria, then this may be a trade off you wish to make, but that is all irrelevant in the context of the discussion of whether JPG is lossy and PNG/TIFF are not.

Please go study some information theory. Ten pounds of information doesn't fit in a five pound sack, no matter how you represent it. It's like why you can't keep gzip'ing a file over and over again to get a smaller file.

To quote you once more, {sigh}. If you want to get into a pi**ing contest about who has the greater expertise in information theory, take it up with the ISO SC29/WG1 committee.