# Is 2 = 1?

Algebra Level 1

What is wrong with the following "proof"?

Let $$a = b=1$$, then $$a=b.$$

• Step 1: $$a^2 = ab$$
• Step 2: $$a^2 - b^2 = ab - b^2$$
• Step 3: $$(a+b)(a-b) = b(a-b)$$
• Step 4: $$a+b= \dfrac{b(a-b)}{a-b}$$
• Step 5: $$a+b = b$$

Conclusion: By substituting, $$a = b = 1 \implies 1+1 = 1 \implies 2 = 1.$$

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