When we have sequences of order type larger than ω, we use transfinite recursion and induction, since our processes use transfinite ordinal numbers. 1.

What are transfinite numbers used for?

These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets.

How do you use a transfinite induction?