Why we should call this : $a,b,c,d,cdots$ sequence better than calling it series with $a,b,c,d,cdots$ are integers?
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I'm confused why mathematical community called $a,b,c,d,cdots$ a sequence better than calling it a series with $a,b,c,d,cdots$ are integers , In addition to that they provided interactive website for Sloan $2008$ under this name " Encyclopedia of integer sequence however terms of sequence here are infinite by the way it satisfies mathematical notion of series better than calling it sequence , Then Why community considered that ?
sequences-and-series definition
edited Aug 30 at 23:37
Bernard
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
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up vote
0
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I'm confused why mathematical community called $a,b,c,d,cdots$ a sequence better than calling it a series with $a,b,c,d,cdots$ are integers , In addition to that they provided interactive website for Sloan $2008$ under this name " Encyclopedia of integer sequence however terms of sequence here are infinite by the way it satisfies mathematical notion of series better than calling it sequence , Then Why community considered that ?
sequences-and-series definition
edited Aug 30 at 23:37
Bernard
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47
add a comment |Â
up vote
0
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favorite
up vote
0
down vote
favorite
I'm confused why mathematical community called $a,b,c,d,cdots$ a sequence better than calling it a series with $a,b,c,d,cdots$ are integers , In addition to that they provided interactive website for Sloan $2008$ under this name " Encyclopedia of integer sequence however terms of sequence here are infinite by the way it satisfies mathematical notion of series better than calling it sequence , Then Why community considered that ?
sequences-and-series definition
edited Aug 30 at 23:37
Bernard
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
I'm confused why mathematical community called $a,b,c,d,cdots$ a sequence better than calling it a series with $a,b,c,d,cdots$ are integers , In addition to that they provided interactive website for Sloan $2008$ under this name " Encyclopedia of integer sequence however terms of sequence here are infinite by the way it satisfies mathematical notion of series better than calling it sequence , Then Why community considered that ?
sequences-and-series definition
sequences-and-series definition
edited Aug 30 at 23:37
Bernard
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
edited Aug 30 at 23:37
Bernard
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
edited Aug 30 at 23:37
Bernard
112k635102
edited Aug 30 at 23:37
Bernard
112k635102
edited Aug 30 at 23:37
Bernard
112k635102
112k635102
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
asked Aug 30 at 23:12
zeraoulia rafik
2,2431828
2,2431828
It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47
add a comment |Â
It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47
It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47
It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47
add a comment |Â
2 Answers
2
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2
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In everyday language "sequence" and "series" are often interchangeable. When mathematicians use words from everyday language to do mathematics they provide them with precise mathematical definitions. We happen to have agreed on "sequence" for
$$
a, b, c, ldots
$$
and "series" for
$$
a + b + c + cdots .
$$
So Sloane's encyclopedia is an encyclopedia of sequences.
Your question suggests that you'd have preferred the other choice, but that's not going to happen.
By analogy, in everyday language "or" sometimes is "or but not both" and sometimes it's "one or both". Mathematicians have decided that in technical work it always means the latter.
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
add a comment |Â
up vote
1
down vote
You may have a slight confusion about what the terms actually mean.
A sequence $(a_n)$ is a ordered countable collection of elements. In the context of $a_n in mathbbR$, for example, we can define a sequence of partial sums,
$$
s_n = sum_k=n_0^n a_n
$$
and this new sequence is called the series of the sequence $a_n$.
So given some numbers $(b_n)$, it is natural to associate them with a sequence. You can also associate them with a series, in which case you need to find the sequence $a_n$ for which $b_n$ will be partial sums...
answered Aug 30 at 23:16
gt6989b
30.7k22248
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
In everyday language "sequence" and "series" are often interchangeable. When mathematicians use words from everyday language to do mathematics they provide them with precise mathematical definitions. We happen to have agreed on "sequence" for
$$
a, b, c, ldots
$$
and "series" for
$$
a + b + c + cdots .
$$
So Sloane's encyclopedia is an encyclopedia of sequences.
Your question suggests that you'd have preferred the other choice, but that's not going to happen.
By analogy, in everyday language "or" sometimes is "or but not both" and sometimes it's "one or both". Mathematicians have decided that in technical work it always means the latter.
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
add a comment |Â
up vote
2
down vote
In everyday language "sequence" and "series" are often interchangeable. When mathematicians use words from everyday language to do mathematics they provide them with precise mathematical definitions. We happen to have agreed on "sequence" for
$$
a, b, c, ldots
$$
and "series" for
$$
a + b + c + cdots .
$$
So Sloane's encyclopedia is an encyclopedia of sequences.
Your question suggests that you'd have preferred the other choice, but that's not going to happen.
By analogy, in everyday language "or" sometimes is "or but not both" and sometimes it's "one or both". Mathematicians have decided that in technical work it always means the latter.
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
add a comment |Â
up vote
2
down vote
up vote
2
down vote
In everyday language "sequence" and "series" are often interchangeable. When mathematicians use words from everyday language to do mathematics they provide them with precise mathematical definitions. We happen to have agreed on "sequence" for
$$
a, b, c, ldots
$$
and "series" for
$$
a + b + c + cdots .
$$
So Sloane's encyclopedia is an encyclopedia of sequences.
Your question suggests that you'd have preferred the other choice, but that's not going to happen.
By analogy, in everyday language "or" sometimes is "or but not both" and sometimes it's "one or both". Mathematicians have decided that in technical work it always means the latter.
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
In everyday language "sequence" and "series" are often interchangeable. When mathematicians use words from everyday language to do mathematics they provide them with precise mathematical definitions. We happen to have agreed on "sequence" for
$$
a, b, c, ldots
$$
and "series" for
$$
a + b + c + cdots .
$$
So Sloane's encyclopedia is an encyclopedia of sequences.
Your question suggests that you'd have preferred the other choice, but that's not going to happen.
By analogy, in everyday language "or" sometimes is "or but not both" and sometimes it's "one or both". Mathematicians have decided that in technical work it always means the latter.
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
answered Aug 30 at 23:19
Ethan Bolker
36.4k54299
36.4k54299
add a comment |Â
add a comment |Â
up vote
1
down vote
You may have a slight confusion about what the terms actually mean.
A sequence $(a_n)$ is a ordered countable collection of elements. In the context of $a_n in mathbbR$, for example, we can define a sequence of partial sums,
$$
s_n = sum_k=n_0^n a_n
$$
and this new sequence is called the series of the sequence $a_n$.
So given some numbers $(b_n)$, it is natural to associate them with a sequence. You can also associate them with a series, in which case you need to find the sequence $a_n$ for which $b_n$ will be partial sums...
answered Aug 30 at 23:16
gt6989b
30.7k22248
add a comment |Â
up vote
1
down vote
You may have a slight confusion about what the terms actually mean.
A sequence $(a_n)$ is a ordered countable collection of elements. In the context of $a_n in mathbbR$, for example, we can define a sequence of partial sums,
$$
s_n = sum_k=n_0^n a_n
$$
and this new sequence is called the series of the sequence $a_n$.
So given some numbers $(b_n)$, it is natural to associate them with a sequence. You can also associate them with a series, in which case you need to find the sequence $a_n$ for which $b_n$ will be partial sums...
answered Aug 30 at 23:16
gt6989b
30.7k22248
add a comment |Â
up vote
1
down vote
up vote
1
down vote
You may have a slight confusion about what the terms actually mean.
A sequence $(a_n)$ is a ordered countable collection of elements. In the context of $a_n in mathbbR$, for example, we can define a sequence of partial sums,
$$
s_n = sum_k=n_0^n a_n
$$
and this new sequence is called the series of the sequence $a_n$.
So given some numbers $(b_n)$, it is natural to associate them with a sequence. You can also associate them with a series, in which case you need to find the sequence $a_n$ for which $b_n$ will be partial sums...
answered Aug 30 at 23:16
gt6989b
30.7k22248
You may have a slight confusion about what the terms actually mean.
A sequence $(a_n)$ is a ordered countable collection of elements. In the context of $a_n in mathbbR$, for example, we can define a sequence of partial sums,
$$
s_n = sum_k=n_0^n a_n
$$
and this new sequence is called the series of the sequence $a_n$.
So given some numbers $(b_n)$, it is natural to associate them with a sequence. You can also associate them with a series, in which case you need to find the sequence $a_n$ for which $b_n$ will be partial sums...
answered Aug 30 at 23:16
gt6989b
30.7k22248
answered Aug 30 at 23:16
gt6989b
30.7k22248
answered Aug 30 at 23:16
gt6989b
30.7k22248
answered Aug 30 at 23:16
gt6989b
30.7k22248
30.7k22248
add a comment |Â
add a comment |Â
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It seems like you are thinking sequence = finite, series = infinite? Actually it's sequence = an ordered list of numbers, series = a sum of a sequence. They can be either infinite or finite (although this might vary depending on the definitions given in whatever source you are reading.)
– Jair Taylor
Aug 30 at 23:47