Two plus two equals six

  ¡@

Assignment of values

a = 6,   b = 4,   c = 5


Steps in the proof

Step 1. Equality

 a + b = 2c

Step 2. Multiply both sides by (a - b)

(a + b) (a - b) = 2c(a - b)

Step 3. Multiply out

a2 - b2 = 2ac - 2bc

Step 4. Add b2 to each side

a2 = 2ac + b2 - 2bc

Step 5. Subtract 2ac from each side

a2 - 2ac = b2 - 2bc

Step 6. Add c2 to each side

a2 - 2ac + c2 = b2 - 2bc + c2

Step 7. Factor

(a - c)2 = (b - c)2

Step 8. Take the square root

a - c = b - c

Step 9.  Add c to both sides

a = b

Step 10. Conclusion

6 = 4

6 = 2 + 2





Comments:

I found this in an old mathematics textbook.

Apparently, in the latter part of the 20th century, many algebra teachers liked to give their students this presentation of 2 + 2 = 6 on the final exam. They would then ask the students to go through each of the ten steps, and point out any errors they could find.

Needless to say, this was quite a challenge to many students who did not have a firm grasp of fundamental mathematical principles.

What about you? Can you find any errors in the ten steps given here?

If you can, please let me know.


Sincerely,

Richard
Nei Hu District
Taipei, Taiwan