Difference between revisions of "Fallacious proof/2equals1"
(I read this "proof" in a magazine a long time ago) |
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=== Explanation === | === Explanation === | ||
− | The trick in this argument is when we divide by <math>a^{2}-ab</math>. Since <math>a=b</math>, <math>a^2-ab = 0</math>, and dividing by [[zero (constant) | zero]] is | + | The trick in this argument is when we divide by <math>a^{2}-ab</math>. Since <math>a=b</math>, <math>a^2-ab = 0</math>, and dividing by [[zero (constant) | zero]] is undefined. |
== Proof 2 == | == Proof 2 == | ||
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=== Explanation === | === Explanation === | ||
− | The | + | The given series does not converge. Therefore, manipulations such as grouping terms before adding are invalid. |
− | [[ | + | |
+ | ''[[Fallacious_proof#2_.3D_1 | Back to main article]]'' |
Latest revision as of 07:29, 5 June 2013
The following proofs are examples of fallacious proofs, namely that .
Contents
[hide]Proof 1
Let .
Then we have
(since )
(adding to both sides)
(factoring out a 2 on the LHS)
(dividing by )
Explanation
The trick in this argument is when we divide by . Since , , and dividing by zero is undefined.
Proof 2
Explanation
The given series does not converge. Therefore, manipulations such as grouping terms before adding are invalid.