Can a sequence be undefined at a point? [duplicate]
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This question already has an answer here:
Are undefined terms allowed in a sequence?
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A sequence which is a mapping from $mathbb{N} to mathbb{R}$.
For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?
real-analysis sequences-and-series
edited Nov 17 at 9:34
Brahadeesh
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
up vote
2
down vote
favorite
This question already has an answer here:
Are undefined terms allowed in a sequence?
3 answers
A sequence which is a mapping from $mathbb{N} to mathbb{R}$.
For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?
real-analysis sequences-and-series
edited Nov 17 at 9:34
Brahadeesh
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
This question already has an answer here:
Are undefined terms allowed in a sequence?
3 answers
A sequence which is a mapping from $mathbb{N} to mathbb{R}$.
For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?
real-analysis sequences-and-series
edited Nov 17 at 9:34
Brahadeesh
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
This question already has an answer here:
Are undefined terms allowed in a sequence?
3 answers
A sequence which is a mapping from $mathbb{N} to mathbb{R}$.
For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?
This question already has an answer here:
Are undefined terms allowed in a sequence?
3 answers
real-analysis sequences-and-series
real-analysis sequences-and-series
edited Nov 17 at 9:34
Brahadeesh
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
edited Nov 17 at 9:34
Brahadeesh
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
edited Nov 17 at 9:34
Brahadeesh
5,90942058
edited Nov 17 at 9:34
Brahadeesh
5,90942058
edited Nov 17 at 9:34
Brahadeesh
5,90942058
5,90942058
asked Nov 17 at 8:40
Sashin Chetty
222
asked Nov 17 at 8:40
Sashin Chetty
222
asked Nov 17 at 8:40
Sashin Chetty
222
222
marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45
add a comment |
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45
add a comment |
2 Answers
2
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up vote
7
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If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
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up vote
1
down vote
If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:
$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$
Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.
answered Nov 17 at 10:33
GuySa
416313
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
add a comment |
up vote
7
down vote
If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
add a comment |
up vote
7
down vote
up vote
7
down vote
If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
answered Nov 17 at 8:43
Joey Kilpatrick
1,183422
1,183422
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
add a comment |
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
2
2
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
+1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
– Dave L. Renfro
Nov 17 at 8:47
add a comment |
up vote
1
down vote
If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:
$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$
Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.
answered Nov 17 at 10:33
GuySa
416313
add a comment |
up vote
1
down vote
If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:
$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$
Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.
answered Nov 17 at 10:33
GuySa
416313
add a comment |
up vote
1
down vote
up vote
1
down vote
If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:
$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$
Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.
answered Nov 17 at 10:33
GuySa
416313
If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:
$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$
Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.
answered Nov 17 at 10:33
GuySa
416313
answered Nov 17 at 10:33
GuySa
416313
answered Nov 17 at 10:33
GuySa
416313
answered Nov 17 at 10:33
GuySa
416313
416313
add a comment |
add a comment |
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 17 at 8:45