I asked this question a while back on the NB forum. I don't remember what the outcome was mainly because I think it was inconclusive.
If you build 100 million cells into 400 million wouldn't that technically be 2 generations, 800 would be 3 and so on.
The way I tend to look at it is every time I use a slurry because alot of the cell count is there and not as much yeast growth has to occur so the same yeast is put to work again. I'm not sure how oftern they die and regen during fermentation so I may be off here but that's my current view of it.
Biologically and philosophically, you are 100% correct. All life comes from pre-existing life.
However, it appears that the "generations" term is used amongst brewers to indicate how many "brew cycles" the yeast has been through. "Brew cycles" meaning "how many times the yeast culture has been used to make a batch of beer." The concern is the potential contamination of the original culture (by bacteria and wild yeast) as well as spontaneous mutations within the culture. Most of us count the way Sean and Denny do (from zero; so the first batch of beer = the first generation).
Some big breweries may go 20-40 brew cycles (or "generations.") but it is recommended by some that homebrewers should not use a yeast culture more than 3-5 brew cycles, even if their "sanitation" is pristine. That advice is probably wise as I don't have laminar air flow hoods, rigid temp controls, SS fermenters and CIP processes like the big brewers do. Plus, a fresh batch of yeast is only about $5-6 bucks. Using really aged yeast that hasn't been put through a starter or is several generations old is risking an infection or off flavors in your beer--it just isn't worth it. At this time, for me, it is less work to just buy another fresh batch periodically than to do all the yeast ranching and acid washing that yeast farmers do to ensure purity of their cultures.