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

(I read this "proof" in a magazine a long time ago) |
m |
||

Line 29: | Line 29: | ||

=== 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]]'' |

## Revision as of 15:04, 21 July 2009

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 illegal.

## Proof 2

### Explanation

The given series does not converge. Therefore, manipulations such as grouping terms before adding are invalid.