# 2=0?

Algebra Level 3

In the proof below, in which step does the first mistake occur?

• Step 1. $$\ 2 = 1 + 1$$
• Step 2. $$\ 2 = 1 + \sqrt{1}$$
• Step 3. $$\ 2 = 1 + \sqrt{(-1)(-1)}$$
• Step 4. $$\ 2 = 1 + \sqrt{(-1)}$$$$\sqrt{(-1)}$$
• Step 5. $$\ 2 = 1 + (i)(i)$$
• Step 6. $$\ 2 = 1 + (-1)$$
• Step 7. $$\ 2 = 0$$
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