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## MODERN GEOMETRY

by: Cassidy Grimes

25

0

2

# MODERN GEOMETRY MATH 532

Cassidy Grimes

GPA 3.51

Ma Filaseta

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COURSE
PROF.
Ma Filaseta
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Cassidy Grimes on Monday October 26, 2015. The Class Notes belongs to MATH 532 at University of South Carolina - Columbia taught by Ma Filaseta in Fall. Since its upload, it has received 25 views. For similar materials see /class/229525/math-532-university-of-south-carolina-columbia in Mathematics (M) at University of South Carolina - Columbia.

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Date Created: 10/26/15
4 L1 53 MATH 5327361 LECTURE 2 Finish Previous Notes Assignment Problems 1 2 8 9 and 10 from Homework 1 Components of an Axiomatic Systems i Unde ned Terms points lines ii De ned Terms parallel iii Axioms iv A system of logic if A or B is true and if not A is true then B is true V Theorems De nition 1 An axiomatic system is consistent if there is not in the system any two axioms any axiom and theorem or any two theorems that contradict each other Comment Start example below De nition 2 An axiom in an axiomatic system is independent if it cannot be proved from the other axioms If each axiom in the axiomatic system is independent then the axiomatic system is said to be independent Comment Continue example below De nition 3 An axiomatic system is complete if every statement containing unde ned or de ned terms of the system can be proved valid or invalid Comments A complete axiomatic system uniquely determines what the system is There is a unique model up to isomorphisms that is described by the axiomatic system It is impossible to add a new independent axiom to a complete axiomatic system Finish example Example Axiom 1 There exist exactly 4 points Axiom 2 Given any two distinct points there is exactly one line that they lie on Axiom 3 Given any line there are exactly 2 points on it Questions 0 What might be de ned terms here 0 What might be unde ned terms here o Is the axiomatic system consistent How do we show this What if the answer were different 0 Are the axioms independent How do we justify our answer What if the answer were different 0 Is this axiomatic system complete How do we justify this What if the answer were different Describe incidence tables and isomorphisms

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