Consider two ‘postulates’ given below:
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.\
Do these postulates contain any undefined terms ? Are these postulates consistent? Do they follow from Euclid’s postulates ? Explain.
Yes! These postulates contain two undefined terms: Point and Line.
Yes! These postulates are consistent because they deal with two different situations (i) say that given two points A and B, there is a point C lying on the line in between them, (ii) say that given A and B, we can take C not lying on the line through A and B. These ‘postulates’ do not follow from Euclid’s postulates however, they follow from Axiom 5.1.
