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Definition
| if you have the set of all points on a line, then those points can be put into a one to one correspondence with all of the real numbers, in an ordered way, such that, any point may correspond to zero and any other point may correspond to one |
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Term
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Definition
| if you have a pair of points on a line, then there corresponds to that pair of points, exactly one number, called the unique distance between the points |
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Term
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Definition
| if you have two points on a line, for which coordinates have been assigned, then the distance between those two points, is the absolute value of the difference between their coordinates |
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Term
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Definition
| if one a line point B lies between points A and C then the measure of the distance from point A to point B (indicated by AB or mAB) plus the measure of the distance from point B to point C (indicated by BC or mBC) is equal to the measure of the distance from point a to point C (indicated by AC or mAC) this assumption is also called the Segment Addition Assumption and can be represented mathematically as AB + BC= AC or mAB + mBC = mAC |
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Term
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Definition
| the Ruler Postulate can be summarized briefly as follows: to measure a line segment you must attach numbers to the endpoints, and find the unique distance between them, by taking the absolute value of the difference between the two numbers |
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