a puzzle for your thoughts

[Chronoshock]

Induction:
What's required?
Inductive hypothesis : Let P(n) be "given a set of n politicians, if one is a liar, all n are liars"
Base Case : P(1) : If the single politician is a liar, then all n are liars. P(1) is true)
Inductive step : Assume P(n) to prove P(n + 1). Here is where the problem lies. P(n + 1) has not been proved true. P(n + 1) is where you have n+1 politicians. Using P(n) we can say that if one of the first n politicians is a liar, then n-1 other politicians are liars. It says nothing about the (n+1)th politician. In order for an induction proof to hold, one must show that P(n+1) is true and P(n)->P(n+1) making P(n) true for all n>base case.

 

[ArmenK]

Originally posted by: Chronoshock
Induction:
What's required?
Inductive hypothesis : Let P(n) be "given a set of n politicians, if one is a liar, all n are liars"
Base Case : P(1) : If the single politician is a liar, then all n are liars. P(1) is true)
Inductive step : Assume P(n) to prove P(n + 1). Here is where the problem lies. P(n + 1) has not been proved true. P(n + 1) is where you have n+1 politicians. Using P(n) we can say that if one of the first n politicians is a liar, then n-1 other politicians are liars. It says nothing about the (n+1)th politician. In order for an induction proof to hold, one must show that P(n+1) is true and P(n)->P(n+1) making P(n) true for all n>base case.

WINNAR :thumbsup:

 

[SWScorch]

yaaaah I was right! The statement works for 1 politician, but there is no logical reason why it works for > 1 politician. Woohoo 10 extra points! (and I need those points bad)