Thanks again for the detailed answers.

Robert Hoedicke has marked this topic as resolved.

Paolo Giarrusso said:

I would assume that if the induction hypothesis holds for an arbitrary n, it also holds for (S n).

Maybe that's clear by now, but that is never something you can assume: when proving

`∀ n, P n`

by induction for some specific`P`

, you must prove`P (S n)`

assuming only`P n`

, and the only way to do that is by using the properties of your specific`P`

.

You found me out. This is really quite embarrassing. I am glad that the answers to my stupid question yielded much deeper insights (at least for me).

Oh dear, I never meant embarrassment, only to clarify (if necessary) :-|

Last updated: Feb 09 2023 at 00:03 UTC