Question 895892
<pre>
This the famous bogus proof that 2=1.  

1.  {{{a}}}{{{""=""}}}{{{b}}}                We can have two variables equal to each other.

2.  {{{a^2}}}{{{""=""}}}{{{ab}}}              We multiply both sides by a.

3.  {{{a^2-b^2}}}{{{""=""}}}{{{ab-b^2}}}       We subtract {{{b^2}}} from both sides

4.  {{{(a-b)(a+b)}}}{{{""=""}}}{{{b(a-b)}}}   We factor both sides. 

5.  {{{a+b}}}{{{""=""}}}{{{b}}}              We divide both sides by (a-b)

6.  {{{b+b}}}{{{""=""}}}{{{b}}}              We substitute b for a since a=b

7.  {{{2b}}}{{{""=""}}}{{{b}}}               We combine like terms on the left

8.  {{{2}}}{{{""=""}}}{{{1}}}                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</pre>