FOR THE STUDENT OF MATHEMATICS
DEMONSTRATION CLUB FILE XXVI


PURPOSE: To demonstrate that for real number x:

                    XXVI.     x's additive inverse is unique.



DEMONSTRATION:      STATEMENTS                                           REASONS



                1.     x + ( -x ) = 0  so -x is an inverse of x       1.     Additive Inverse Property X   p + ( -p ) = 0

                2.     Suppose x + ( y ) = 0   for -x ≠ y             2.     Supposition that x has two inverses.

                3.     x + ( -x ) = x + ( y )                                  3.     Property XIX Both sides equal 0 so equal each other.

                4.     - x = y                                                     4.     Property XXII Subtract x from both sides in 3.

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



A real number has exactly one additive inverse.







Would you like to demonstrate Property XXVII. ?

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

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