# Proof that one equals two

### Given: a = b

**Invalid?** |
**Step** |
**Justification** |

Check |
a = b |
Given |

Check |
ab = b^2 |
Multiply both sides by b |

Check |
ab - a^2 = b^2 - a^2 |
Subtract a^2 from both sides |

Check |
a(b-a) = (b + a)(b - a) |
Factor both sides |

Check |
a = b + a |
Divide by (b - a) |

Check |
a = a + a |
Given a = b |

Check |
a = 2 * a |
Simple addition |

Check |
1 = 2 |
Divide by a |

#### Can you spot the fallacy in this proof?

There is only one illegal step in this proof. Click on the button next to the step you think is invalid.
The correctness of your choice will be displayed after a brief waiting period. The correct
answer has the shortest waiting period.

Created by Andrew Freed, arf132@psu.edu on April 7, 2002.

Modified by Andrew Freed, arf132@psu.edu on April 15, 2002.

Development of this resource was sponsored by the Penn State Fund for
Excellence in Learning and Teaching (FELT), project "Java-based
Teaching of Mathematics in Information Sciences and Technology",
supervised by Frank Ritter and David Mudgett.