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# 1=2: A Proof using Beginning Algebra

The Fallacious Proof:
• Step 1: Let a=b.
• Step 2: Then a^2 = ab,
• Step 3: a^2 + a^2 = a^2 + ab,
• Step 4: 2 a^2 = a^2 + ab,
• Step 5: 2 a^2 - 2 ab = a^2 + ab - 2 ab,
• Step 6: and 2 a^2 - 2 ab = a^2 - ab.

• Step 7: This can be written as 2 (a^2 - a b) = 1 (a^2 - a b),
• Step 8: and cancelling the (a^2 - ab) from both sides gives 1=2.

See if you can figure out in which step the fallacy lies. When you think you've figured it out, click on that step and the computer will tell you whether you are correct or not, and will give an additional explanation of why that step is or isn't valid.

See how many tries it takes you to correctly identify the fallacious step!

This page last updated: May 26, 1998
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu

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