the real number system -13 o, 1, 2, 3… 1/2 0.333 π

The Real Number System

-13 O, 1, 2, 3…

1/2

0.333

π

Natural NumbersNatural Numbers

1 2 3 4 5 6 7 8 9 10 . . .

Also call COUNTING COUNTING NUMBERSNUMBERS

WHOLE NUMBERSWHOLE NUMBERS

1 2 3 4 5 6 7 8 9 10 …… 00

Natural Natural NumbersNumbers

WHOLE NUMBERSWHOLE NUMBERS

1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7. . . .6, 7. . . .

OO, 1, 2, 3, 4, 5, 6, 7 . . . .

The Real Number SystemThe Real Number System

INTEGERS

OO 1 2 3 4 5 1 2 3 4 5

6 7. . . 6 7. . . -7 –6 –5 –4 –3 –-7 –6 –5 –4 –3 –2 –1 2 –1

Natural NumbersNatural Numbers

WHOLE NUMBERSWHOLE NUMBERS

1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7. . . .6, 7. . . .

OO, 1, 2, 3, 4, 5, 6, 7 . . . .

The Real Number SystemThe Real Number System

INTEGERS

-7, -6, -5, -4, -3, -2, -1,-7, -6, -5, -4, -3, -2, -1, O O, 1, 2, 3, 4, 5, 6, 7 . . . .

RATIONAL NUMBERSRATIONAL NUMBERS

0 1 2-1-2-2.33

-3½

RATIONAL NUMBERSRATIONAL NUMBERSincludeinclude

•½, ¾ Fractions

• 0.3333… Repeating Decimals

• .5, .12 Terminating decimals

Natural NumbersNatural Numbers

WHOLE NUMBERSWHOLE NUMBERS

1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7. . . .6, 7. . . .

OO, 1, 2, 3, 4, 5, 6, 7 . . . .

The Real Number SystemThe Real Number System

Rational Numbers

-7, -6, -5, -4, -3, -2, -1,-7, -6, -5, -4, -3, -2, -1, O O, 1, 2, 3, 4, 5, 6, 7 . . . .

INTEGERS

. . -4,. . -4, -3 -3¼¼,, -3, -2, -3, -2, 0.50.5 -1, -1, O O, 1, ½, 2, 2.33, 3, 4. .

Irrational NumbersIrrational Numbers

o

Don’t Behave like the other Subsets

IRRATIONAL NUMBERSIRRATIONAL NUMBERSincludeinclude

• Pi or π 3.141592653589753……..

• Non-repeating non terminating decimals1.21211211121111211111….

• Square roots that are not “Perfect Squares” √17

WHOLE NUMBERS

O, 1, 2, 3, 4. . .  

INTEGERS

. . . -5, -4, -3, -3, -2, -1, 0, 1, 2, 3, 4, 5 . . .

2.34526765…IRRATIONAL IRRATIONAL NUMBERSNUMBERS

π √99

NATURAL NUMBERS

1, 2, 3…. 

REAL NUMBER SYSTEM

RATIONAL NUMBERS

. . . -3, -2.5, -2, -1, 0, 1, ½, 2, 2.33. . .