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  3. suppose we replace incidence axiom 4 with the foll

Suppose we replace Incidence Axiom 4 with the following: Given any line, there are at least...

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Advance Math

Suppose we replace Incidence Axiom 4 with the following: Givenany line, there are at least three distinct points that lie onit.

What is the smallest number of points in a model for thisgeometry? More precisely, find a number n such that every model hasat least n points and there is at least one model that has only npoints, and explain why your answer is correct.

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4.5 Ratings (893 Votes)
To construct the minimal geometry where the parallel postulateholds and where every line has at least three points lets againstart with the bare minimum of any model three pointsA B Candtheir associated lines ABAC and BCbelow added image    See Answer
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