F3:    Unique Solution to    x+a=b

Rosenlicht states this consequence as follows:  "For any [real numbers]  a,  b  [...] the equation  x+a=b has one and only one solution."  (see ita-2-1-7-pg17)  Rosenlicht's proof and test of solution are illustrated below with the justifications for each step explicitly given in the second column of the output matrices.


In the above cited paragraph, Rosenlicht makes the following additional points:  (1) If we let  b=a  in  F3.1,  then we get  x=0,  which shows that the neutral element for addition is unique.  (2) If we let  b=0  in  F3.1,  then we get  x=(-a),  which shows that, for any real number  a,  the additive inverse is unique.

Definition of Subtraction



Converted [ in part ] by Mathematica      December 4, 2007