Jovan claims that 4 = 5.
He tries to prove his obviously false claim that 4 = 5 in the following line of thought:
Where is the error?
The mistake lies in the penultimate line of the train of thought. In this row, Jovan divides both sides by (5x – 4y):
The second line of his calculations correctly states that 5x = 4y. This is equivalent to the equation 5x – 4y = 0, so Jovan is effectively dividing both sides by 0, which is, of course, not allowed.
The proof that 4 = 5 is thus exposed as false.
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.