Here is an obviously false theorem, together with a (nonobviously) bogus proof. Identify precisely the flaw in the argument and explain where the proof fails. False Theorem: 1 = 0. Proof. Consider...

Here is an obviously false theorem, together with a (nonobviously) bogus proof. Identify precisely the flaw in the argument and explain where the proof fails.

False Theorem: 1 = 0.

Proof. Consider the four shapes in Figure 4.34(a), and the two arrangements thereof in Figure 4.34(b). (See below.

The area of the triangle in the first configuration is 13 5/2 = 65/2, as it forms a right triangle with height 5 and base 13. But the second configuration also forms a right triangle with height 5 and base 13 as well, and therefore it too has area 65/2. But the second configuration has one unfilled square in the triangle, and thus we have