0

This question has been always intrigued me.
Why proof by Induction is admissible/acceptable ?
We use this type of proof nearly every where and some times It's the easiest way of proof.

Javi
  • 6,263
Itay.V
  • 406
  • What do you mean? Do you understand how induction works? Or are you asking something else? – Zaros Nov 16 '16 at 22:07
  • 1
    Have a look at (http://math.stackexchange.com/q/928323). – Jean Marie Nov 16 '16 at 22:09
  • Are you using 'admissible' as a formal, defined term here? If so, what definition? If not, can you please further explain what you're asking for? – Nick Peterson Nov 16 '16 at 22:12
  • Bye_World, sorry, i've tried to look for it but probably not clearly enough. any way, my question is why can we use induction as a valid proof indeed ? i can understand why it works Intuitively but i was sure why its valid. i will try to check that post, i guess it being explained there why. Thanks. – Itay.V Nov 16 '16 at 22:30

1 Answers1

0

It's admissible because it's defined as an axiom of our arithmetic. It was chosen as an axiom because it's a proof method that works - so much so that there are variants that apply even when you're not working with the natural numbers, as long as a few other properties hold.

If you have a problem with why it works, feel free to ask it and I can try to elaborate.

ConMan
  • 24,300
  • well i Intuitively understand why it works but i just keep missing the point of why we can be sure its a valid way of proof, how do you know that for every set of proofs and theorems that being proven by Induction are valid ? how do you know there isnt a theorem that cant be mistakly proven by induction ? – Itay.V Nov 16 '16 at 22:32
  • Because it's baked into the structure of the natural numbers and the way we are able to write statements of arithmetic. It happens to be equivalent to saying that the natural numbers are well-ordered, which is a specific property that has been assigned to them.

    It's possible to pose a theorem that appears to be provable by induction, but where there is a fault in the proof, but the problem is in the misapplication of induction, not in induction itself.

     – ConMan Nov 16 '16 at 22:44