Does it make sense to talk about limit in this case?
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Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited Jan 5 at 18:58
zipirovich
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
$endgroup$
add a comment |
$begingroup$
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited Jan 5 at 18:58
zipirovich
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
$endgroup$
add a comment |
$begingroup$
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited Jan 5 at 18:58
zipirovich
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
$endgroup$
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
real-analysis limits
edited Jan 5 at 18:58
zipirovich
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
edited Jan 5 at 18:58
zipirovich
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
edited Jan 5 at 18:58
zipirovich
11.3k11731
edited Jan 5 at 18:58
zipirovich
11.3k11731
edited Jan 5 at 18:58
zipirovich
11.3k11731
11.3k11731
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
asked Jan 5 at 16:44
Юрій ЯрошЮрій Ярош
1,079615
1,079615
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
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add a comment |
$begingroup$
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
$endgroup$
add a comment |
$begingroup$
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
$endgroup$
add a comment |
$begingroup$
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
$endgroup$
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
answered Jan 5 at 16:48
John OmielanJohn Omielan
4,7962216
4,7962216
add a comment |
add a comment |
$begingroup$
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
$endgroup$
add a comment |
$begingroup$
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
$endgroup$
add a comment |
$begingroup$
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
$endgroup$
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
answered Jan 5 at 18:21
Hans LundmarkHans Lundmark
36.1k564115
36.1k564115
add a comment |
add a comment |
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