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#1
 
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Function -
01-14-2008
, 03:56 PM
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David Cressey wrote: vldm10 wrote: David BL wrote: This however doesn't change the fact that most authors define a (mathematical) relation as a set of ordered tuples, which means a function is not a relation (assuming, as most do, that a function has a defined domain and codomain). I don't understand how the conclusion follow from the premise. I am afraid that you don't understand above conclusion because you don't understand what function is. What makes you think that? Definition1 A function from A to B is a rule that assigns, to each member of set A, exactly one member of set B. Is this good or bad definition for a function? If you thing that this is good definition for a function then please explain why this is good definition, else please explain why it is not good definition. Your answer on my question will be also answer on your question. |
How did you assess David's lack of understanding 'function'?
What gave you that impression?
This is not the first time that 'function' popped up as pivotal
to some misunderstandings in cdt - but I fail to see where
the unclarity is right now.
(cdt glossary
Quote:
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[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: General A purpose or use. Math A binary mathematical relation with at most one b for each a in (a,b). Software A subroutine, procedure, or method. notes: every operator is a function every function is a relation Please be specific. |
--
What you see depends on where you stand.
#2
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#3
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#4
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#5
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#6
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#7
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#8
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#9
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). |
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."
You might even add something about calling D and C domain and codomain
respectively, although that might open up a whole new can of worms.
Of course, I'm still convinced that the c.d.t. glossary is a waste of
time, but there you go. ;-)
-- Jan Hidders
#10
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vldm10 wrote: *> David Cressey wrote:*>> vldm10 wrote: *>>>> David BL wrote: *>>>>> This however doesn't change the fact that most authors *>>>>> define a (mathematical) relation as a set *>>>>> of ordered tuples, which means a function is not a relation *>>>>> (assuming, as most do, that a function has *>>>>> a defined domain and codomain). *>>>> I don't understand how the conclusion follow from the premise. *>>> I am afraid that you don't understand above conclusion *>>> *because you don't understand what function is. *>> What makes you think that? * *> Definition1 * *A function from A to B is a rule that assigns, *> to each member of set A, exactly one member of set B. * *> Is this good or bad definition for a function? *> If you thing that this is good definition for a function then *> please explain why this is good definition, *> else please explain why it is not good definition. *> Your answer on my question will be also answer on your question. This is getting silly. Did you even read the question? How did you assess David's lack of understanding 'function'? What gave you that impression? This is not the first time that 'function' popped up as pivotal to some misunderstandings in cdt - but I fail to see where the unclarity is right now. (cdt glossary *> [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: * *> General *> A purpose or use. *> Math *> A binary mathematical relation with at most *> one b for each a in (a,b). *> Software *> A subroutine, procedure, or method. * *> notes: *> every operator is a function *> every function is a relation * *> Please be specific. -- What you see depends on where you stand. |
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.
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