# Difference between revisions of "Fallacious proof/2equals1"

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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 == |

## Latest revision as of 08:29, 5 June 2013

The following proofs are examples of fallacious proofs, namely that .

## Contents

## 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.