Mathematics
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.
Euclid's Geometry
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Answer
Using Euclid’s axioms to check these postulates :
Yes, these postulates contain undefined terms like point and line.
These two statements are consistent as they talk about two different situations meaning different things.
These statements do not follow Euclid’s postulates but one of the axioms about “Given any two points, a unique line that passes through them” is followed.
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