In Proofs
In an axiomatic treatment of geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or else be defined in terms of an isometry of a line (used as a coordinate system).
Segments play an important role in other theories. For example, a set is convex if the segment that joins any two points of the set is contained in the set. This is important because it transforms some of the analysis of convex sets to the analysis of a line segment.
Read more about this topic: Line Segment
Famous quotes containing the word proofs:
“Would you convey my compliments to the purist who reads your proofs and tell him or her that I write in a sort of broken-down patois which is something like the way a Swiss waiter talks, and that when I split an infinitive, God damn it, I split it so it will stay split, and when I interrupt the velvety smoothness of my more or less literate syntax with a few sudden words of bar- room vernacular, that is done with the eyes wide open and the mind relaxed but attentive.”
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“Trifles light as air
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—William Shakespeare (1564–1616)