# Two Equals One

## An Advanced Mathematics Lesson Starter Of The Day

 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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