The Numbe r Lin e an d Rea l Number s
Let's consider numbers and the number line again, as well as review what you have
already learned through junior high school.
Point 0 an d another point E ar e given on a single straight line / . Excluding poin t
0, lin e / i s divided into two parts on either side of point O. Th e part that contains point
E i s called the positive side, and the part without point E i s called the negative side.
negative side——«—-~~^ ^----«---«- - positive side
The points on line / correspon d to numbers in the following way .
Point O correspond s t o the number 0. Fo r any point on the positive or negative side,
let s b e its distance from point O , taking segment OE a s the unit of length. Whe n the
point is on the positive side, it corresponds to the positive number s, and when it is on the
negative side, it corresponds to the negative number -s.
! 0\ E
-s 0
In this way, every point on / correspond s to a unique number: different point s
correspond to different numbers . Th e number that corresponds to point P i s called the
coordinate of point P, and the notation P(x) signifie s tha t x i s the coordinate of point
P. Poin t P i s sometimes referred t o as the point x fo r short .
When each point on line / i s indicated by the number which is its coordinate, / i s
called th e number line , O i s the origin, and E i s the unit point . Th e coordinat e o f
the origin is 0, and the coordinate of the unit point is 1. Number s expressed as points on
the number line are called real numbers .
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