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Proof: Your IQ = Einstein's IQ

Consider this proof...

Let Y equal your IQ and E equal Einstein's IQ

Let S = E + Y

Multiplying both sides by E-Y: SE - SY = E2 - Y2

Rearranging: Y2 - SY = E2 - SE

Add S2/4 to both sides: Y2 - SY + S2/4 = E2 - SE + S2/4

Factoring both sides: (Y - S/2)2 = (E - S/2)2

Taking square root of both sides: Y - S/2 = E - S/2

Adding S/2 to both sides: Y = E

That is, your IQ is equal to Einstein's IQ.

Your Task: Find the error in this proof...or perhaps there is no error, and both IQs are equal.


Source: C. Denbow & V. Goedicke. Foundations of Mathematics. 1959, pp. 197-198

Hint: Check each line...is there an algebra error?

From the start, suppose E > Y (or possibly Y > E) ...is there a problem with the proof?


Solution Commentary: Remember, when taking a square root, it could be either positive or negative.