Difference between revisions of "Fallacy"
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m (→2 = 1: this should fix it) |
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Then we have | Then we have | ||
| − | <math> a^2 = ab </math> (since <math>a=b</math>) | + | <div style="text-align:center"><math> a^2 = ab </math> (since <math>a=b</math>)</div> |
| − | <math> 2a^2 - 2ab = a^2 - ab </math> (adding <math>a^2-2ab</math> to both sides) | + | <div style="text-align:center"><math> 2a^2 - 2ab = a^2 - ab </math> (adding <math>a^2-2ab</math> to both sides)</div> |
| − | <math> 2(a^2 - ab) = a^2 - ab </math> (factoring out a 2 on the [[LHS]]) | + | <div style="text-align:center"><math> 2(a^2 - ab) = a^2 - ab </math> (factoring out a 2 on the [[LHS]])</div> |
| − | <math> 2 = 1 </math> (dividing by <math>a^2-ab</math>) | + | <div style="text-align:center"><math> 2 = 1 </math> (dividing by <math>a^2-ab</math>)</div> |
[[Fallacious proof/2equals1 | Explanation]] | [[Fallacious proof/2equals1 | Explanation]] | ||
Revision as of 20:33, 11 March 2007
A fallacious proof is a an attempted proof that is logically flawed in some way. The fact that a proof is fallacious says nothing about the validity of the original proposition.
Common false proofs
The fallacious proofs are stated first and then links to the explanations of their fallacies follow.
2 = 1
Let 
.
Then we have
(since )
(adding 
to both sides)
(factoring out a 2 on the LHS)
(dividing by 
)All horses are the same color
We shall prove that all horses are the same color by induction on the number of horses.
First we shall show our base case, that all horses in a group of 1 horse have the same color, to be true. Of course, there's only 1 horse in the group so certainly our base case holds.
Now assume that all the horses in any group of 
horses are the same color. This is our inductive assumption.
Using our inductive assumption, we will now show that all horses in a group of 
horses have the same color. Number the horses 1 through . Horses 1 through must be the same color as must horses 
through . It follows that all of the horses are the same color.
