FOR THE STUDENT OF MATHEMATICS
DEMONSTRATION CLUB FILE XXVII

PURPOSE: To demonstrate that for real number x ≠ 0:

XXVII.     x's multiplicative inverse is unique.

DEMONSTRATION:      STATEMENTS                                           REASONS

1.     x ( 1 / x ) = 1   so 1 / x is a reciprocal of x ≠ 0       1.   Multiplicative Inverse Property XI   p ( 1 / p ) = 1

2.     Suppose x ( y ) = 1   for 1 / x ≠ y ≠ 0                     2.   Supposition that x has two reciprocals.

3.     x ( 1 / x ) = x ( y )                                                 3.   Property XIX Both sides equal 1 so equal each other.

4.     1 / x = y                                                               4.   Divide x into both sides in 3 [ XXIII, VI, X and VIII ]

5.     x's multiplicatve inverse is unique.                        5.   Statements 2 and 4 form a contradiction.

A nonzero real number has exactly one reciprocal.

Would you like to demonstrate Property XXVIII. ?

Properties:     List #1 Link     List #2 Link     List #3 Link     List #4 Link     List #5 Link   and   Demonstrations