Posted by Alex on Monday, September 26, 2011 at 3:22am.
Find the error in the following proof that all horses are the same color.
CLAIM: In any set of h horses, all horses are the same color.
PROOF: By induction on h.
Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color.
Induction step: For k 1 assume that the claim is true for h = k and prove that it is true for h = k + 1 . Take any set H of k + 1 horses. We show that all the horses in the set are the same color. Remove one horse from this set to obtain the set H1 with just k horses. By the
induction hypothesis, all the horses in H1 are the same color. Now replace the removed horse and remove a dierent one to obtain the set H2. By the same argument, all the horses in H2 are the same color. Therefore all the horses in H must be the same color, and the proof is complete.

computer sciece(Computation Theory)  MathMate, Monday, September 26, 2011 at 6:55am
"...prove that it is true for h = k + 1 . Take any set H of k + 1 horses. We show that all the horses in the set are the same color. Remove one horse from this set to obtain the set H1 with just k horses...."
The induction process requires to prove that given the proposition is true for k, then k+1 is true.
The above prove is proving that given k+1 is true, then k is true. So k decreases, and does not help to prove that k+2 ... is true.
Answer This Question
Related Questions
 maths  A & B together have 132 horses. If 0.25 of the no. of A 's horses = 0....
 math  horses are entered in a race. If two horses are tied for first ...
 math  seven horses are entered in a race. If two horses are tied for first&#...
 mason  seven horses are entered in a race. If two horses are tied for first&#...
 ps 361  there are 16 horses. 8 chickens are white. 7 horses run away. how many ...
 Math  On joes farm there are 99 animals. There are four times as many cows as ...
 Math  joe has a farm with 99 animal, four times as many cows as horses, twice ...
 math please help  One day, a person went to horse racing area, Instead of ...
 math  john has horses and chickens he has 3 less chickens than horses, if you ...
 satistical mobeling  there are 12 horses in a horse show competition. the top ...
More Related Questions