#1
Ok we are supposed to find the fallacy with this proof by induction. I am not quite sure exactly what it is, but I am pretty sure it has something to do with the case of there just being two people. Anyway, please explain this in dumbed down terms if you know where it fails.

Prove everyone has blue eyes by induction

case n=1: I have blue eyes. This is true because I have blue eyes.

Assume Case K: Any group of K people all have blue eyes.

Now prove K+1 to complete induction argument and prove everyone has blue eyes: In any group K+1, you can remove one person and be left with a group of K people. By our assumption in our inductive hypothesis, everyone in the group of K people has blue eyes. Now place the person we removed back in the group and remove a different person. Now we are left with a group of K people with our original removee in the group. By our inductive hypothesis, this group of K people all have blue eyes. Thus everyone has blue eyes. QED

Plz help
#2
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#4
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#5
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#6
Can't you just know that not everyone has blue eyes because K is not all inclusive? Since K doesn't include everyone, and no reason exists to lead you to believe that people outside of group K have blue eyes, you can thus infer that not all people have blue eyes. Because examples exist in the real world that prove the statement that everyone has blue eyes false, you can induce that the statement is false. I think. You can also argue that the population K may not have been picked at random, leaving no validity in the statement.
#8
I'm not stunning at induction but i'll give it a go. i think the problem is with n=1. There is no left and right hand sides of a formula because there is no formula. i believe inductive proof is only possible with algebraic equations.
the logic youve stated seems to make sense, however, what if you didnt have blue eyes? it would then prove that noone had blue eyes.

If i had to guess i would say that an inductive proof just isnt possible.

Edit: good argument metallifan3091
i'll go along with that one too
Last edited by benrochlin at Sep 19, 2009,
#9
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