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  #31  
Old   
mAsterdam
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:26 AM






vldm10 wrote:
Quote:
I think it will be good to have two definitions for the functions in
your glossary.
Definition1 A function from A to B is a rule that assigns, to each
member of set A, exactly one member of set B.

And second definition is similar to Jan's suggestion, but slightly
changed:
Definition2
A function from A to B is a relation between A and B that associates
each element of A with exactly one element of B.

First definition says that a function do something. You can call it
intutive definition of a function. Here the function in fact is a
procedure as you mentioned.
Second definition is set theoretic.
Another difference I see with Jan's is a sense of direction.

How about this:
cdt glossary proposal:

Quote:
[Codomain]
See function, math context.

[Domain]
1. Given a relation R, a domain is a set Sn such
that for each tuple (A1, A2, ...An, ...Am) in R,
An is an element of Sn.

2. A domain is a set of values: for example
"integers between 0 and 255",
"character strings less than 10 characters long",
"dates".
Sometimes used synonymously with type.

3. Domain of a function. See function, math context.



[Function]
For now we have to live with different meanings
of _function_ when talking about databases:
"The function of this function is to get the tuples from B
that are functionally dependant on A."

Three different contexts, but just about the same meaning:

1. General
A purpose or use.

2. Math
A binary mathematical relation over two sets D and C that
associates with each element in D exactly one element in C.
Set D is called the domain of the function, C its codomain.

3. Software
A subroutine, procedure, or method.


In both the math and software context, there is a sense of
direction from domain (input) to codomain (output).
For most purposes, this intuitive picture is good enough:

|------------|
--- x ---- >| f-machine |------ f(x) -----
|------------|

Where x is input in the "f-machine" and f(x) is output.

notes:
every operator is a function
every function is a relation


--
What you see depends on where you stand.




Reply With Quote
  #32  
Old   
mAsterdam
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:26 AM






vldm10 wrote:
Quote:
I think it will be good to have two definitions for the functions in
your glossary.
Definition1 A function from A to B is a rule that assigns, to each
member of set A, exactly one member of set B.

And second definition is similar to Jan's suggestion, but slightly
changed:
Definition2
A function from A to B is a relation between A and B that associates
each element of A with exactly one element of B.

First definition says that a function do something. You can call it
intutive definition of a function. Here the function in fact is a
procedure as you mentioned.
Second definition is set theoretic.
Another difference I see with Jan's is a sense of direction.

How about this:
cdt glossary proposal:

Quote:
[Codomain]
See function, math context.

[Domain]
1. Given a relation R, a domain is a set Sn such
that for each tuple (A1, A2, ...An, ...Am) in R,
An is an element of Sn.

2. A domain is a set of values: for example
"integers between 0 and 255",
"character strings less than 10 characters long",
"dates".
Sometimes used synonymously with type.

3. Domain of a function. See function, math context.



[Function]
For now we have to live with different meanings
of _function_ when talking about databases:
"The function of this function is to get the tuples from B
that are functionally dependant on A."

Three different contexts, but just about the same meaning:

1. General
A purpose or use.

2. Math
A binary mathematical relation over two sets D and C that
associates with each element in D exactly one element in C.
Set D is called the domain of the function, C its codomain.

3. Software
A subroutine, procedure, or method.


In both the math and software context, there is a sense of
direction from domain (input) to codomain (output).
For most purposes, this intuitive picture is good enough:

|------------|
--- x ---- >| f-machine |------ f(x) -----
|------------|

Where x is input in the "f-machine" and f(x) is output.

notes:
every operator is a function
every function is a relation


--
What you see depends on where you stand.


Reply With Quote
  #33  
Old   
mAsterdam
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:26 AM



vldm10 wrote:
Quote:
I think it will be good to have two definitions for the functions in
your glossary.
Definition1 A function from A to B is a rule that assigns, to each
member of set A, exactly one member of set B.

And second definition is similar to Jan's suggestion, but slightly
changed:
Definition2
A function from A to B is a relation between A and B that associates
each element of A with exactly one element of B.

First definition says that a function do something. You can call it
intutive definition of a function. Here the function in fact is a
procedure as you mentioned.
Second definition is set theoretic.
Another difference I see with Jan's is a sense of direction.

How about this:
cdt glossary proposal:

Quote:
[Codomain]
See function, math context.

[Domain]
1. Given a relation R, a domain is a set Sn such
that for each tuple (A1, A2, ...An, ...Am) in R,
An is an element of Sn.

2. A domain is a set of values: for example
"integers between 0 and 255",
"character strings less than 10 characters long",
"dates".
Sometimes used synonymously with type.

3. Domain of a function. See function, math context.



[Function]
For now we have to live with different meanings
of _function_ when talking about databases:
"The function of this function is to get the tuples from B
that are functionally dependant on A."

Three different contexts, but just about the same meaning:

1. General
A purpose or use.

2. Math
A binary mathematical relation over two sets D and C that
associates with each element in D exactly one element in C.
Set D is called the domain of the function, C its codomain.

3. Software
A subroutine, procedure, or method.


In both the math and software context, there is a sense of
direction from domain (input) to codomain (output).
For most purposes, this intuitive picture is good enough:

|------------|
--- x ---- >| f-machine |------ f(x) -----
|------------|

Where x is input in the "f-machine" and f(x) is output.

notes:
every operator is a function
every function is a relation


--
What you see depends on where you stand.


Reply With Quote
  #34  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #35  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #36  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #37  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #38  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #39  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM



On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


Reply With Quote
  #40  
Old   
Marshall
 
Posts: n/a

Default Re: Function - 01-15-2008 , 08:55 AM






On Jan 15, 6:25 am, mAsterdam <mAster... (AT) vrijdag (DOT) org> wrote:
Quote:
Jan Hidders wrote:

[snip]

(cdt glossary

[Function]
...
Math
A binary mathematical relation with at most
one b for each a in (a,b).

This "at most one b for each a in (a,b)" makes me cringe!

Irritation about the status quo is a starting point
to many improvements. I am sure the "Software" subentry (you
snipped it) makes functional programming adepts curl
their toes as well - I'll keep it until somebody provides
a better text.

Moreover, it
seems to describe partial functions, which is not what is usually
understood under "function". I would make that:

"A binary mathematical relation over two sets D and C that associates
with each element in D exactly one element in C."

I like it.
I'll post a proposal for replacement in my answer to Vladimir.
To the native english speakers: is 'that' correct in Jan's sentence?
Yes.

There are different kinds of things that variously get called
functions:

total functions, partial functions, multifunctions, aggregate
functions

Often "function" by itself means "total function" but sometimes it
doesn't.

It seems the difference between a total function and a partial
function is
just in what we want to call the domain. Division over the domain
(integer, integer) is partial; division over the domain (integer,
nonzero integer)
is total. What's up with that?

Some things out there produce more than one result, or a stream of
results. Sometimes these are called multifunctions and sometimes
generators.

Then we have things like sum() avg() etc. Aggregate functions.


Marshall


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