Start with a simple identity,
a = b
Multiply each side by a:
a^2 = a b
Subtract b^2 (b squared) from each side of the equality:
a^2 – b^2 = a b – b^2
Using high school algebra, factor out the term (a – b) from each side:
(a + b) (a – b) = b (a – b)
Divide each side by (a – b), effectively canceling out the term from each side, leaving:
(a + b) = b
Per our opening equality, substitute a for b:
a + a = a
Combine terms:
2 a = a
Factor out the a’s, and you’re left with:
2 = 1
Where did we go wrong???
Tuesday, April 15, 2008
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