Consider two positive numbers \(a\) and \(b\) that are equal: | $$ a = b $$ |

Multiply both sides of this equation by \(a\), | $$ a^{2}=ab $$ |

Subtract \(b^2\) from both sides. | $$ a^{2}-b^{2}=ab-b^{2} $$ |

Factorise both sides | $$ (a-b)(a+b)=b(a-b) $$ |

Divide both sides by \( (a - b) \). | $$a+b=b $$ |

As \( a = b \) substitute \(b\) for \(a\). | $$ b+b=b $$ |

Collect like terms | $$ 2b=b $$ |

Divide both sides by \( b \). | $$2 = 1 $$ |

How can this be? | $$???$$ |

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