Interval
Notation
Subsets of real
numbers
can be represented using
interval notation. Suppose that
0
and b are two real numbers such that
a < b.
Inierval Notation Graph
The open interval (a,b) represents the set
of real numbers between, but not including,
a and b.
(o,b):{"la<x<b}
x is greater
than
a la < xl
and
x is
less
lhan
b lx
<bl.
#]
q (a,b) b
T[e
pareatheses
in
fhe
graph
and
in
interval notalion
indicale
thal a and 1,, ihe
endpoinls, are
excluded from fhe inierval.
The cfosed
interval
la.b)represents
the
set
real numbers
between,
and
including,
a and
fo,bl:{xla<x=b}
x is
greater
lhan or
equal lo a la < xl
and
x is
less than
or equal to
b lx < bl.
#'a [a,h] b
Ihe square brackelr
in
lle
graph
and in
inferval nolalion
indicate
lhsl
a and b, the endpoints,
ere
included
in
lhe interval.
a \a,
r)
The
parenthesis
indicales lhat
a
is excluded
from
the inlerval.
_.+---l+.r (--,bl b
The square
bracket
indicates
that b is included
in the inferyal.
^f
(Jl
h.
The infinite interval (o, *) represents
the
set
of
real
numbers
that are greater
than
a.
(o,*) : {" i
x > a}
The
infinity
symbol
does
not
rePresenl a
real number,
lt
indicales
fhat
lhe interval
exfends
indefinilely
to
the right.
The infinite interval (-oo, bl represents
the
set
of
real
numbers
that are less
than
or equal to b.
(-*, D]
: {x l, = b}
fhe
negalive
infinity
symbol
indicstes
that
fhe interval
extendc iadcfinitely
to
the left.
