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5:17
Study.com
Yuanxin (Amy) Yang Alcocer
The Axiomatic System: Definition & Properties
In mathematics, the axiomatic system refers to the statements and rules used to develop and prove theorems. Explore the definition and properties of the axiomatic system, including consistency, independence, and completeness. Understand how an axiom compares to an axiomatic system.
20K views
Jan 28, 2014
Axiomatic System Examples
SOLVED: I understand how to prove this using 3 points. How do I prove itwhen adding a fourth?Consider the axiomatic system and theorem below:Axiom 1: If there is a pair of points, then they are on a linetogether.Axiom 2: If there is a line, then there must be at least twopoints on it.Axiom 3: There exist at least three distinct points.Axiom 4: If there is a line, then not all of the points can beon it,Theorem 1: Each point is on at least two distinct lines.
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