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Most of us use this fact without thinking about it. To prove the formula, we use the results of a previous proof.

♦ To start, we identify A and B as:

A = 2 - 1 and B = 2 - 1

Then since A and B both equal 1 we have:

A x B = A x B and (2 - 1) x ( 2 - 1 ) = 1

The expression above right can be written as:

[ (2) + (- 1) ]^{2} = 1

This result has the form (C + D)^{ 2} with C = 2 and D = -1 .

By a previous proof we have:

(C + D)^{2} = C^{2} + 2 CD + D^{2}

Therefore, using the right side we have,

(2 x 2) + 2 x [(2) x (-1)] + (-1) x (-1) = 1

Which equals:

4 - 4 + [(-1) x (-1)] = 1

Collected, we obtain:

( -1 ) x ( -1 ) = 1 Q.E.D.

This proof depended upon a previous proof. In thermodynamics (as in algebra) small understandings are combined to become larger understandings.

Most of us use this fact without thinking about it. To prove the formula, we use the results of a previous proof.

Premise presently unwritted!