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Honestly, 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 ago
  Sure. 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 ago
      That's a perfect demonstration of the difference between epistemic induction (unprovable) and mathematical induction (provable).
      • RiderOfGiraffes 16y ago
        Er, actually it's not. It is mathematical induction, but with a broken case.
    • johnaspden 16y ago
      Beautiful. Thank you.