As many people, we came across the following photo:
In this mathematical “proof” the author tries to convince us that there is an error in math and it can be demonstrated using the above example. The steps taken by this person are the following:
- The proof starts by defining
a = b).
- Then, it multiplies both sides with
awhich results to
a^2 = ab.
- Next, it subtracts from both sides
b^2and we get
a^2-b^2 = ab-b^2.
- Following, it extracts the common multiplier of both sides
(a+b)(a-b) = b(a-b).
- Here’s the nice part, the author divides both sides with
(a-b)which results to
a+b = b.
a = b, it replaces
aon the left side with a
band produces this state
b+b = b => 2b = b.
- Finally, it divides by
bboth sides which results to
2 = 1.
The reason that this proof is false is because in step 5, where it divides both sides with
(a-b) it really is dividing both sides with
0 (since we know for sure that
a = b from step 1) which it cannot be defined as a valid division. So everything from step 5 and forward are invalid and thus the proof is wrong.