**Theorem.** Among all positive integers, the integer 1 is the largest.

Proof | |

Step 1. | Take any integer $n \neq 1$. |

Step 2. | Since $n^2 > n$, it is not the largest positive integer. |

Step 3. | Therefore, 1 is the largest integer. |

What is the error (if any) in the above proof?

Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. - Sherlock Holmes

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