THERMO Spoken Here! ~ J. Pohl  ©  ( A1160~11/15)( A1220 -  1.02 Position the First Vector)

Prove: (-1) x (-1) = 1

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.

Prove: (-1) x (-1) = 1

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!