WebIt’s clear from the question and from your discussion with @DonAntonio that you don’t actually understand the induction step of the argument. Web1 has the same color as all horses in B, which includes h 3, and h 2 has the same color as all horses in A, which also includes h 3. So, the color of h 1, h 2 and h 3 are all the same, and so the color of all horses in K = A [B must be the same. So, by induction we have proven P(n) for all positive integers n. Discussion Note this proof is ...
What is wrong with the following "proof" that all horses are the same …
All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect. This example was originally raised by George Pólya in a … See more The argument is proof by induction. First, we establish a base case for one horse ($${\displaystyle n=1}$$). We then prove that if $${\displaystyle n}$$ horses have the same color, then $${\displaystyle n+1}$$ horses … See more The argument above makes the implicit assumption that the set of $${\displaystyle n+1}$$ horses has the size at least 3, so that the two proper See more • Unexpected hanging paradox • List of paradoxes See more WebWe will show that all horses are the same color by showing that the statement “any set of N horses must consist of horses of a single color” is true for an value of N. Base case: N=1. “Any set of 1 horse must consist of horses of a single color”. This statement is self-evident. ritchie bbc2
Episode 3: All Horses Are the Same Color - YouTube
WebInductive Step: Assume that P(k) is true, so that all the horses in any set of k horses are the same colour. Consider any k +1 horses; number theses as horses 1,2,3,...,k,k +1. Now the firstk of these horses must have the same color, and the last k … WebNote that P (1) is true, since for any set containing a single horse, all the horses in that set have the same color, namely the color of that single horse. Next, let m> 1 and assume that P (m) is true, i.e., that for any set of m horses, all the horses in the set are the same color. We prove that P (m+1) is true. WebExpert Answer. "All horses are the same color." Let's prove that for a set of whatever finite sets of horse, all horses are the same color. From the logical point of view, it is ∀n ≥ 1,P (n) where P (n) states that in all sets of n horses, all horses are the same color. Basis step (Base case): is true, i.e., just one horse. ritchie battle pittsburgh