Difference between revisions of "Fallacious proof/all horses are the same color"
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Our base case is not the appropriate base case: if one could show that every pair of horses has the same color (the result for <math>n = 2</math>), the fact that all horses have the same color would follow. Unfortunately, the case <math>n = 2</math> does not follow from the case <math>n = 1</math>. The first horse is the same color as itself, and so is the second horse, but there is no overlap. | Our base case is not the appropriate base case: if one could show that every pair of horses has the same color (the result for <math>n = 2</math>), the fact that all horses have the same color would follow. Unfortunately, the case <math>n = 2</math> does not follow from the case <math>n = 1</math>. The first horse is the same color as itself, and so is the second horse, but there is no overlap. | ||
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Revision as of 22:45, 7 August 2006
Our base case is not the appropriate base case: if one could show that every pair of horses has the same color (the result for 
), the fact that all horses have the same color would follow. Unfortunately, the case does not follow from the case 
. The first horse is the same color as itself, and so is the second horse, but there is no overlap.
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