The person before made a mistake in their proof.

1. x = y

2. xy = y^2

3. xy - x^2 = y^2 - x^2

4. x(y - x) = (y + x)(y - x)

So far so good.

4.5. x = (y + x)(y - x)/(y - x)] is what they did to get to step 5, which says:

5. x = y + x

This is wrong though. since x = y, y -x = 0, and so you can't divide by y - x.

1. x = y

2. xy = y^2

3. xy - x^2 = y^2 - x^2

4. x(y - x) = (y + x)(y - x)

So far so good.

4.5. x = (y + x)(y - x)/(y - x)] is what they did to get to step 5, which says:

5. x = y + x

This is wrong though. since x = y, y -x = 0, and so you can't divide by y - x.

by mathisfun
March 17, 2008

1. x = y

2. xy = y^2

3. xy - x^2 = y^2 - x^2

4. x(y - x) = (y + x)(y - x)

5. x = y + x

6. x = x + x

7. x = 2x

8. 1 = 2

QED

2. xy = y^2

3. xy - x^2 = y^2 - x^2

4. x(y - x) = (y + x)(y - x)

5. x = y + x

6. x = x + x

7. x = 2x

8. 1 = 2

QED

As proven, 1 = 2, thus 0 = 1, etc. And so for any number i, there is an equivalent j that is not equal to i.

This is further explained in the Identity Theft Theorem.

This is further explained in the Identity Theft Theorem.

by SAH aka the GSH
October 16, 2006