Is it appropriate to 'build up' your findings in a paper? I'm working on a Mathematics paper at the moment, and my first finding was fairly specific. The next finding generalised the first finding, and my third finding generalised my second finding.
My first and second findings are therefore just special cases of my third finding, but they are still significant.
Is it appropriate for me to write all 3 findings in the paper and build upwards from the first, including the proofs for the the 1st and 2nd finding and generalising as we go, or should I just include the 3rd finding only, and point out afterwards that there are a couple of significant special cases that follow from it (namely finding 1 and finding 2)?
(Although including all 3 findings would lengthen the paper, I also feel that it would provide more of an insight into how I found result 3, rather than just mysteriously producing it from scratch.)
Either way could be made to work, but consider:
If the proof methods of the three are essentially the same, then the first way would be boring (possibly).
But if the second builds on the first (etc) by using different insights and methodologies, then the first way might well be superior.
Don't just consider the progression of results but of the progression of proofs and, especially, insights, that get you to the final result.
And if the latter is the case, make sure you emphasize those insights. They might (and often do) lead to developing other ideas.