Homework SourseUsing these definitions fixing a point O on a line l and ass
Using these definitions, fixing a point O on a line l, and assuming the neutral plane satisfies the axioms of continuity:
-prove the operation of addition on line l is commutative and associative
-prove for any natural number n, n*A = A+A+...+A n times that given any A on l not equal to O and any B on l there exists a natural number n such that
absolute value (nA)> absolute value (B)
Solution
-prove the operation of addition on line l is commutative and associative.
From definition 3 we could say that if l is a line and O is apoint on l then
then for any A on l we can write A + O = O +A , this is a representation of the commutative law of addition
which say that m+n = n+m
Form definition 1 we could ay that if A,B and C are three points on a line l then
AB + BC = AC
or A(B-C)= -BC
or A(C-B)= BC
this conforms with the asosiative law of addition which says:
a+(b+c) = b+(a+c) = c+(a+b)
Hence proved that the operation of addition on line l is commutative and associative
