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Lebl-Basic-Analysis-I
· Problem 3.1.7
Continuous Functions
Mathematics · limits-of-functions
Problem
Find an example of a function
f
:
[
−
1
,
1
]
→
R
f : [-1, 1] \to \mathbb{R}
f
:
[
−
1
,
1
]
→
R
, where for
A
:
=
[
0
,
1
]
A := [0, 1]
A
:=
[
0
,
1
]
, we have
f
∣
A
(
x
)
→
0
f|_A(x) \to 0
f
∣
A
(
x
)
→
0
as
x
→
0
x \to 0
x
→
0
, but the limit of
f
(
x
)
f(x)
f
(
x
)
as
x
→
0
x \to 0
x
→
0
does not exist. Note why you cannot apply Proposition 3.1.15.
Related theory
Limits And Continuity Of Real Valued Functions
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