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 EY: SE  SY = E^{2}  Y^{2}
Rearranging: Y^{2}  SY = E^{2}  SE
Add S^{2}/4 to both sides: Y^{2}  SY + S^{2}/4 = E^{2}  SE + S^{2}/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. 197198
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.
