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n-ary operations
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ruben safir
Dec 11, 2014, 11:15:08 AM12/11/14
to
I have this quote fro a textbook
6.2.2 The CARTESIAN PRODUCT (CROSS PRODUCT)
Operation
Next, we discuss the CARTESIAN PRODUCT operation—also known as CROSS
PRODUCT or CROSS JOIN—which is denoted by ×. This is also a binary set
opera-
tion, but the relations on which it is applied do not have to be union
compatible. In
its binary form, this set operation produces a new element by combining
every
member (tuple) from one relation (set) with every member (tuple) from
the other
relation (set). In general, the result of R(A1, A2, ..., An) × S(B1, B2,
..., Bm) is a rela-
tion Q with degree n + m attributes Q(A1, A2, ..., An, B1, B2, ..., Bm),
in that order.
The resulting relation Q has one tuple for each combination of
tuples—one from R
and one from S. Hence, if R has nR tuples (denoted as |R| = nR), and S
has nS tuples,
then R × S will have nR * nS tuples.
The n-ary CARTESIAN PRODUCT operation is an extension of the above concept,
which produces new tuples by concatenating all possible combinations of
tuples
from n underlying relations.
What is an n-ary operation? I see this repeadely but I am not
understanding its meaning.
Ruben
6.2.2 The CARTESIAN PRODUCT (CROSS PRODUCT)
Operation
Next, we discuss the CARTESIAN PRODUCT operation—also known as CROSS
PRODUCT or CROSS JOIN—which is denoted by ×. This is also a binary set
opera-
tion, but the relations on which it is applied do not have to be union
compatible. In
its binary form, this set operation produces a new element by combining
every
member (tuple) from one relation (set) with every member (tuple) from
the other
relation (set). In general, the result of R(A1, A2, ..., An) × S(B1, B2,
..., Bm) is a rela-
tion Q with degree n + m attributes Q(A1, A2, ..., An, B1, B2, ..., Bm),
in that order.
The resulting relation Q has one tuple for each combination of
tuples—one from R
and one from S. Hence, if R has nR tuples (denoted as |R| = nR), and S
has nS tuples,
then R × S will have nR * nS tuples.
The n-ary CARTESIAN PRODUCT operation is an extension of the above concept,
which produces new tuples by concatenating all possible combinations of
tuples
from n underlying relations.
What is an n-ary operation? I see this repeadely but I am not
understanding its meaning.
Ruben
Gene Wirchenko
Dec 11, 2014, 12:15:20 PM12/11/14
to
On Thu, 11 Dec 2014 11:15:12 -0500, ruben safir <ru...@mrbrklyn.com>
wrote:
>I have this quote fro a textbook
>
>6.2.2 The CARTESIAN PRODUCT (CROSS PRODUCT)
>Operation
>Next, we discuss the CARTESIAN PRODUCT operation—also known as CROSS
>PRODUCT or CROSS JOIN—which is denoted by ×. This is also a binary set
>opera-
>tion, but the relations on which it is applied do not have to be union
>compatible. In
>its binary form, this set operation produces a new element by combining
>every
>member (tuple) from one relation (set) with every member (tuple) from
>the other
>relation (set). In general, the result of R(A1, A2, ..., An) × S(B1, B2,
>..., Bm) is a rela-
R is an n-ary operation. It has n operands.
S is an m-ary operation. It has m operands.
>tion Q with degree n + m attributes Q(A1, A2, ..., An, B1, B2, ..., Bm),
>in that order.
Q is an (n+m)-ary operation. It has n+m operands.
>The resulting relation Q has one tuple for each combination of
>tuples—one from R
>and one from S. Hence, if R has nR tuples (denoted as |R| = nR), and S
>has nS tuples,
>then R × S will have nR * nS tuples.
>The n-ary CARTESIAN PRODUCT operation is an extension of the above concept,
>which produces new tuples by concatenating all possible combinations of
>tuples
>from n underlying relations.
>What is an n-ary operation? I see this repeadely but I am not
>understanding its meaning.
The operation takes n operands.
Sincerely,
Gene Wirchenko
wrote:
>I have this quote fro a textbook
>
>6.2.2 The CARTESIAN PRODUCT (CROSS PRODUCT)
>Operation
>Next, we discuss the CARTESIAN PRODUCT operation—also known as CROSS
>PRODUCT or CROSS JOIN—which is denoted by ×. This is also a binary set
>opera-
>tion, but the relations on which it is applied do not have to be union
>compatible. In
>its binary form, this set operation produces a new element by combining
>every
>member (tuple) from one relation (set) with every member (tuple) from
>the other
>relation (set). In general, the result of R(A1, A2, ..., An) × S(B1, B2,
>..., Bm) is a rela-
S is an m-ary operation. It has m operands.
>tion Q with degree n + m attributes Q(A1, A2, ..., An, B1, B2, ..., Bm),
>in that order.
>The resulting relation Q has one tuple for each combination of
>tuples—one from R
>and one from S. Hence, if R has nR tuples (denoted as |R| = nR), and S
>has nS tuples,
>then R × S will have nR * nS tuples.
>The n-ary CARTESIAN PRODUCT operation is an extension of the above concept,
>which produces new tuples by concatenating all possible combinations of
>tuples
>from n underlying relations.
>What is an n-ary operation? I see this repeadely but I am not
>understanding its meaning.
Sincerely,
Gene Wirchenko
ruben safir
Dec 11, 2014, 1:05:33 PM12/11/14
to
On 12/11/2014 12:15 PM, Gene Wirchenko wrote:
> R is an n-ary operation. It has n operands.
>
> S is an m-ary operation. It has m operands.
>>blink<<
> R is an n-ary operation. It has n operands.
>
> S is an m-ary operation. It has m operands.
Like a derivation of the work unary and binary?
James K. Lowden
Dec 11, 2014, 9:13:23 PM12/11/14
to
Banks" (Codd, 1970):
"The term relation is used here in its accepted mathematical
sense. Given sets S1, S2, ? ? ? , Sn (not necessarily distinct), R is a
relation on these n sets if it is a set of n-tuples each of which has
its first element from S1, its second element from S2, and so on. We
shall refer to Sj as the jth domain of R. As defined above, R is said
to have degree n. Relations of degree 1 are often called unary, degree
2 binary, degree 3 ternary, and degree n n-ary."
--jkl
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