[rsj_hn]

> But consider for the moment the question of why you are convinced that induction is valid. There is no proof of induction's validity. The epsilon delta thing is a definition, not a proof, and serves, effectively, to invert infinity into an infinitesimal. I am on firm ground with these statements, like it or not.

I'm afraid these statements are a mishmash of some correct and incorrect statements, and a logical argument like that is considered incorrect.

* Yes, the definition of limit is a definition.

* The definition of limit has nothing to do with induction or infinity. I'm honestly baffled why these three distinct concepts are being conflated.

* For well ordered sets, induction is just reductio ad absurdum in which you assume the smallest element does not satisfy a condition and then show this to be incorrect because the next smallest element must meet the condition and it's satisfication means the next larger element must meet it as well. There is a valid question as to whether every set can be well-ordered, which is an axiom, but for countable sets, which is where virtually all induction arguments are used, no axiom of choice is needed to use induction-style arguments.

* The statement "to invert infinity into an infinitesimal." is gibberish.