This the famous bogus proof that 2=1.
1. We can have two variables equal to each other.
2. We multiply both sides by a.
3. We subtract from both sides
4. We factor both sides.
5. We divide both sides by (a-b)
6. We substitute b for a since a=b
7. We combine like terms on the left
8. We divide both sides by b
It looks as though we have proved this proves that 2 equals 1. But there is a
flaw. The flaw is in step 5. The rule for dividing both sides of an equation
is:
"Both sides of an equation can be divided by the same non-zero number."
However (a-b) is zero in disguise because a = b. So step 5 is an error.
Edwin
