2=1?  math puzzle
Suppose: a = b
It then follows that
a * a = a * b
a^2 = a * b
a^2  b^2 = a * b  b^2
(a  b) * (a + b) = (a  b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1
Is this derivation really correct? Or is there somewhere a mistake? If so, where?
It then follows that
a * a = a * b
a^2 = a * b
a^2  b^2 = a * b  b^2
(a  b) * (a + b) = (a  b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1
Is this derivation really correct? Or is there somewhere a mistake? If so, where?
Explanation
Of course the derivation should be wrong. 2 is not equal to 1. The mistake is in step
(a  b) * (a + b) = (a  b) * b
to
a + b = b
This step is not allowed if a = b. Because then you are dividing by zero. And dividing by zero is nonsense.
(a  b) * (a + b) = (a  b) * b
to
a + b = b
This step is not allowed if a = b. Because then you are dividing by zero. And dividing by zero is nonsense.
