2 1 NUMBERSANDEXPRESSION S

REAL NUMBER S

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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

O

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 .