# Proof that 2=1

## Proof

1) . Given.

2) . Multiply both sides by a.

3) . Subtract from both sides.

4) . Factor both sides.

5) . Divide both sides by

6) . Substitute for .

7) . Addition.

8) . Divide both sides by .

## Error

Usually, if a proof proves a statement that is clearly false, the proof has probably divided by zero in some way.

In this case, the quantity of is as , since one cannot divide by zero, the proof is incorrect from that point on.

**Thus, this proof is false.**

## Note:

If this proof were somehow true all of mathematics would collapse. Simple arithmetic would yield infinite answers. This is why one cannot divide by zero.