Begonias have incomplete flowers by definition because they are either male or female, so any one particular flower doesn't have all particular parts. Flower nomenclature always gets screwy, because begonias have tepals, not petals, and sepals are something else entirely!

Getting back to the subject, the extra tepals occurring during doubling come from the conversion of other flower parts into tepals. This happens more frequently with male flowers, but female flowers also double. The structures converted, however, are usually reproductive parts, so a double male flower has no pollen producing parts and is sterile, a "mule" as it were. The doubling of a plant's flowers is usually unstable to a greater or lesser degree. The double male flowers of tuberous begonias often revert back to single flowers at the end of the season.

This is fortunate if your goal is seed production, such as hybridization work or the production of F1 or F2 seed such as the 'Nonstop" series. And, naturally, the genetics of the pollen from the single flower is identical to the rest of the double-flowered plant, even though the tuber produces double flowers the next spring again. The result of all this is that a species may produce double flowers, but usually those individuals are sterile because they have no reproductive parts. Naturally occurring doubles do happen, but die out of the specie's gene pool unless asexually reproduced by man.

Begonias, unless "doubles", usually have four tepals. Doubling is a "generic" term because it can involve much more than doubling to eight tepals - any number can happen within physical limits. Begonia octopetala comes to mind because of the "eight petals" but this is the "normal" count for the species and the necessary reproductive structures are there so it is not technically a double. I've had male flowers double on rex hybrids, but always a fluke and not stable. Doubling can occur as a "shock" reaction to chemicals or physical stress, like heat.(Doug Hahn:Mason, Ohio)