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.