THERMO Spoken Here! ~ J. Pohl © | TOC NEXT ~ 7 |
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 = C2 + 2 CD + D2
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.