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The open interval (a,b) represents the set of real numbers between, but not including, a and b. x is greater than a la < xl and x is less lhan b lx <bl.
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x is greaterthana la < xl
a n d
x i s l e s sl h a nb l x < b l.
q ( a , b ) b
T[e pareatheses
in fhegraph
a n di n i n t e r v a ln o t a l i o ni n d i c a l e
thal a and1,, ihe endpoinls,are
e x c l u d e df r o mf h ei n i e r v a l.
x is greaterlhanor equal lo a la
< xl
a n d
x i s l e s st h a n o r e q u a lt o b l x
< b l.
a
[ a , h ]
b
Ihesquarebrackelrin lle graph
a n di n i n f e r v a ln o l a l i o n i n d i c a t e
lhsla andb, theendpoints, ere
i n c l u d e di n l h ei n t e r v a l.
a
\ a , r )
Theparenthesis indicaleslhat a
is excluded fromthe inlerval.
T h es q u a r e b r a c k e ti n d i c a t e s
t h a tb i s i n c l u d e d i n t h ei n f e r y a l.
^ f
( J l
Theinfinitysymbol does
not
r e P r e s e n la r e a ln u m b e r , l t
indicalesfhatlheinterval
exfendsindefinilely to theright.
fhenegaliveinfinitysymbol
indicstesthatfheinterval
extendciadcfinitely to theleft.
Parenthesesand Bracketsin Interval Notation
Parenthesesindicateendpointsthatarenot includedin aninterval.Square
bracketsindicate endpoints that are included in an interval.
Thble 1.5 lists nine possibletypes of intervalsused to describesubsetsof real
numbers.
Table 1.5 Intervals on the Real Number Line
I Let a and b be real numberssuchthat a < b.
:
I
i Interval
I
I Notation Set-BuilderNotation
: Graph
i @ , b )
f r t
I Q. D I
i
,,
La b)
r l
{ t l o <
x < b }
t a b
t r l , r = x = b \
'
i
I
'.
a b
{ -. l n < x < b }
{ " l n < x = b l
a b
( a , o o )
{
x l x > a \
l #. r
L '
i
[ 4 ,
o o )
{ x l x
a }
' o - , u )
t. t l r \ u - i
r t
i
( - - , o o
) { , r l x
i s a r e a l n u m b e r } o r R
1
(setof all real numbers) ,
x ' h l
.. r
t. Y l. t
l 7 i
.l