<table><tr><th>From:</th><th>jeffrey E. &lt;jeevacation@gmail.com&gt;</th></tr><tr><td>Sent:</td><td>Monday, December 4, 2017 12:59 PM</td></tr><tr><td>To:</td><td>Misha Gromov</td></tr></table>

why is transfinite recursion <https://en.wikipedia.=rewikiirransfinite_recursion> a good model for und=rstanding - the proof that the result is well-defined uses transfi=ite induction. Let F denote a (class) function F to be defin=d on the ordinals. The idea now is that, in defining F(a) for =n unspecified ordinal a, one may assume that F(3) is alre=dy defined for all a < a =nd thus give a formula for F(a) in terms of these F(Q=B2). It then follows by transfinite induction that there is one and only one function satisfying the recursion formula up to and including a.

(more will be given later): define function F by letting F=a) be the smallest ordinal not in the set conversation-id 22029 date-last-viewed 0 date-received 1512392341 flags 8590195713 gmail-label-ids 7 6 remote-id 775029