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Honestly, I think most people who "prove" things using induction don't really understand what they're doing. Then again, most people don't really understand rec
by edanm 16y ago
Honestly, I think most people who "prove" things using induction don't really understand what they're doing. Then again, most people don't really understand recursion either.
- tkahn6 16y agoHonestly, I think most people who "prove" things using induction don't really understand what they're doing Can you explain what you mean by this?
- edanm 16y agoSure. In my experience, most people who go through math classes at a University, not to mention classes in High School, are mostly "blindly" following a template of how to do induction. They don't really understand the principle behind it, why it's a valid proof technique, etc. Put another way, if I used induction incorrectly, I could probably still trick them into thinking it's a valid proof because it looks like induction. The same goes for a lot of things in Mathematics. The same also goes for recursion - most people don't really understand recursion (unless it's used at a "simple" level, like in Tree Recursion).
- lmkg 16y ago> if I used induction incorrectly, I could probably still trick them into thinking it's a valid proof because it looks like induction. You mean like this one? http://en.wikipedia.org/wiki/All_horses_are_the_same_color http://en.wikipedia.org/wiki/All_horses_are_the_same_color My college calculus professor used this example when she was teaching induction.
- jemfinch 16y agoThat's a perfect demonstration of the difference between epistemic induction (unprovable) and mathematical induction (provable).
- RiderOfGiraffes 16y agoEr, actually it's not. It is mathematical induction, but with a broken case.
- johnaspden 16y agoBeautiful. Thank you.
- ent 16y agoThis sounds more like a case of people not understanding what proving by induction is (and as a consequence, not doing so) rather than them proving by induction and and not understanding what they are doing.