WOLFRAM
|
DEMONSTRATIONS PROJECT
Bolzano's Theorem
a
1
.
5
b
4
.
5
B
o
l
z
a
n
o
'
s
t
h
e
o
r
e
m
s
t
a
t
e
s
t
h
a
t
i
f
f
i
s
a
c
o
n
t
i
n
u
o
u
s
f
u
n
c
t
i
o
n
i
n
t
h
e
c
l
o
s
e
d
i
n
t
e
r
v
a
l
[
a
,
b
]
w
i
t
h
f
(
a
)
a
n
d
f
(
b
)
o
f
o
p
p
o
s
i
t
e
s
i
g
n
,
t
h
e
n
t
h
e
r
e
i
s
a
c
i
n
t
h
e
o
p
e
n
i
n
t
e
r
v
a
l
(
a
,
b
)
s
u
c
h
t
h
a
t
f
(
c
)
=
0
.
