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Unformatted text preview: Lecture 8: Coordinates on the line June 13, 2010 We’re going to leave logic for the time being in order to think about geometry. Coordinate systems (plural!) on the line In Lecture 1, talked about the number line. To refresh your memory, we started with a line, chose a unit of distance, a point on the line (called the origin) and a direction on the line (called the positive direction). We then labelled the points on the line with numbers in such a way that: 1) the origin was assigned 0, 2) the points on the positive side of the origin were labelled with positive numbers and 3) the distance between any two points, as measured by the unit bracerightbigg = braceleftbigg the absolute value of the difference between their labels. Once points have been labelled in this way, we have a coordinate system on the line. Each point has a name that is a number, and each number names a point. Different numbers name different points and different points have different numbernames. The difficulty is that the coordinate system was arbitrary. To make the coordinate system, we had to make some choices—an origin, a positive direction and a unit of length. But what if, at another time or for another purpose, someone else chooses a different origin, a different direction and a different unit of length? How can we relate her coordinate system to ours? This is not an unusual problem. You already saw an instance of it in the Fahrenheit and Celsius markings on the thermometer....
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This note was uploaded on 11/23/2011 for the course MATH 6302 taught by Professor Madden during the Summer '11 term at LSU.
 Summer '11
 MADDEN
 Math, Logic, Geometry

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