Rim, Sorry you really lost me somewhere.
Yes I think I may have lost most people

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Essentially we are saying the same thing with a couple of exceptions.
Dpi isn't about pixel size or quality.
DPI is not about pixel size or
display output but it is about
print quality / output size.
Pixel dimensions determine the final output quality, all things being equal.
Depends what you are outputting too (monitor or printer).
More pixels, more image quality. A PPI change DOES NOT change the image size.
Yes it does. More pixels = bigger image unless you change the PPI ratio. Changing the PPI ratio without constraining the picture size will change the size of the displayed image. If you have an image that is 100x100 pixels and = 1" x 1" at 100 PPI(for example) the having a ppi of 50 will change it to 2" x 2" (2"x50PPI = 100 pixels). Having a PPI of 200 with the same image will reduce its size to 1/2"x1/2". This is size as relates to the capacity of the monitor in use. This will not change print size unless the software used is changing the DPI to match the PPI. The image resolution will remain the same but this is not the same as physical size.
A 2304 x 1728 (4mp) image, is still the same file size at 72dpi or 300 dpi.
If you are not constraining the size then of course. You have the same number of pixels to report on so why would the file size change. I think the problem is that you are measuring the image size by pixels rather than a static measurement like inches or centimetres. Physical size cannot be denoted by number of pixels. It depends on the PPI of the display device as to how big the picture will be physically displayed.
Dpi really is important when printing only. DPI is printing terminology. PPI is computer screen resolution. Though to often simplify things they can mean the same thing in usage.
Yep we both agree on this 100%
At 72dpi, the 2304 x 1728 4mp image will print as 32 inches by 24 inches.
At 300dpi, it prints at 7.68 inches x 5.76 inches. Its still the same file size and resolution, whatever the dpi. Changing the dpi just alters the print dimensions..
It is still the same displayed size if the PPI does not change with the DPI. Just as changing the DPI changes its output format size (i.e. printing), changing the PPI changes its output format size (display on a monitor) but it will not physically change the number of pixels in the image unless you constrain the image size (not resolution).
Large print dimensions (10"x8")and low resolutions (1600x1200) just result in poor pics. (Not enough pixels to cover the area.)
Now this depends on the DPI of the picture as you mentioned above. If a picture is set to 1 DPI it does not matter how many pixels it has, it will still look really bad unless viewed from distance (probably a very long distance

).
I think for the most part this is pretty immaterial as most software allows you to choose to change only the DPI values and therefore they are linking the DPI to PPI and changing both.
There is a nice set of charts
here which give you an idea of monitors PPI stats depending on resolution / size and aspect ratio of the monitor.
Going any further than this is going to drive me insane and I have a reasonable handle on this

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The problem is there are so many variables that will be specific to the users setup. It is very much like colour profiling where it can get very complex.
Bottom line is that if you keep the dpi to between 200 and 300 you will get good quality shots as long as DPI x size in inches for each side is not greater than the pixel resolution for that side. If it is greater then quality will suffer as the difference increases.
The resolution does not determine the final size but the output device does depending on it's Dpi or Ppi ability / setting. Just don't get me started on the DPI / PPI debate on printers and how the number of inks (i.e. 6) relate to DPI but PPI needs to be divided by the number of inks as the six inks are used to make one final colour dot which would be the equivalent of a views monitor pixel

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Guess I really should do some work now.
RB