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Basic Thermodynamics ~ J. Pohl © ~ 2019 | www.ThermoSpokenHere.com (A1160-007) |

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.