if f is monotonic, least fixpoint of f is stationary limit of fα(0), taking α over ordinals
fα is defined by #transfinite induction: fα+1 = f ( fα)
fγ for a limit ordinal γ is least upper bound of fβ for all β ordinals < γ. dual theorem holds for greatest fixpoint.

- If α is any ordinal and X is a set, an α-indexed sequence of elements of X is a function from α to X. #transfinite sequence

- #Transfinite recursion is similar to transfinite induction; however, instead of proving that something holds for all ordinal numbers, we construct a sequence of objects, one for each ordinal.

- Borel hierarchy is used to prove facts about the Borel sets using #transfinite induction on rank.

if f is monotonic, then min fixpoint F of f is stationary limit of fα(0), taking α over ordinals, where fα is defined by #transfinite induction: fα+1 = f ( fα)
fγ for a limit ordinal γ is least upper bound of fβ for all β ordinals < γ. dual theorem for Max F
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Taken as reciprocals, it seemed that the #transfinite numbers ought to provide an immediate basis for a theory of actual infinitesimals. But to #Cantor's mind, such a step was irresponsible and under no circumstances could it be rigorously justified. #Grundlagen

Taken as reciprocals, it seemed that the #transfinite numbers ought to provide an immediate basis for a theory of actual infinitesimals. But to #Cantor's mind, such a step was irresponsible and under no circumstances could it be rigorously justified. #Grundlagen