[Trac] [OpenMath] #43: CD fns1

[OpenMath]

#43: CD fns1
------------------------------+---------------------------------------------
     Reporter:  jauecker      |          Owner:  kohlhase  
         Type:  proposal      |         Status:  new       
     Priority:  major         |      Milestone:  CD3 Draft1
    Component:  OM3 Standard  |        Version:            
   Resolution:                |       Keywords:            
Include_gantt:  0             |   Dependencies:            
   Due_assign:  YYYY/MM/DD    |      Due_close:  YYYY/MM/DD
------------------------------+---------------------------------------------
Old description:

> '''Chris:'''
>

> I use 'range' for the image under the function of of the function's
> domain (IOW, the set of values taken by the function); a synonym for
> 'image'.
>
> I use 'codomain' for the (not a) set containing this 'range' that is
> defined as the set that appears 'on the right-hand side of the arrow'.
> Note that then: different codomain implies different function even if
> they are otherwise identical.
>
> ----------------
>
> It says 'the identity function': does this imply uniqueness, the same
> function for any set?
>
> ----------------
>
> Should we use 'left' and 'right' inverses in K-12 descriptions?
>
> And what is 'right_compose' ???
>
> ----------------
>
> I have never thought of 'lambda' as anything to do with maths, which
> managed for 500 years of specifying functions without it.
>

> '''Michael:'''
>

> >I use 'range' for the image under the function of of the function's
> >domain (IOW, the set of values taken by the function); a synonym >for
> 'image'.
> >
> >I use 'codomain' for the (not a) set containing this 'range' that >is
> defined as the set that appears 'on the right-hand side of the >arrow'.
> >Note that then: different codomain implies different function even >if
> they are otherwise identical.
>
> I do too, but I also know people who say image and range, and it will not
> be easy to change these.
>
> >Should we use 'left' and 'right' inverses in K-12 descriptions?
>
> I tend to agree that we should not, but there is an OM/MathML merging
> issue here. We had decided that we would use the OpenMath CDs of the
> "MathML Compatibility Group" as a basis for the  CMathML3 set. And the CD
> fns1 contained left/right_inverse . By the OpenMath CD rules, we cannot
> just drop symbols from a CD or backwards compatibility reasons.
> Therefore we would have to invent a new CD (e.g. fns3). We will have to
> discuss how to do this.
>
> >And what is 'right_compose' ???
>
> This could be added from what I understand the rules to be.

New description:

 '''Chris:'''


 I use 'range' for the image under the function of of the function's
 domain (IOW, the set of values taken by the function); a synonym for
 'image'.

 I use 'codomain' for the (not a) set containing this 'range' that is
 defined as the set that appears 'on the right-hand side of the arrow'.
 Note that then: different codomain implies different function even if
 they are otherwise identical.

 ----------------

 It says 'the identity function': does this imply uniqueness, the same
 function for any set?

 ----------------

 Should we use 'left' and 'right' inverses in K-12 descriptions?

 And what is 'right_compose' ???

 ----------------

 I have never thought of 'lambda' as anything to do with maths, which
 managed for 500 years of specifying functions without it.


 '''Michael:'''


 >I use 'range' for the image under the function of of the function's
 >domain (IOW, the set of values taken by the function); a synonym >for
 'image'.
 >
 >I use 'codomain' for the (not a) set containing this 'range' that >is
 defined as the set that appears 'on the right-hand side of the >arrow'.
 >Note that then: different codomain implies different function even >if
 they are otherwise identical.

 I do too, but I also know people who say image and range, and it will not
 be easy to change these.

 >Should we use 'left' and 'right' inverses in K-12 descriptions?

 I tend to agree that we should not, but there is an OM/MathML merging
 issue here. We had decided that we would use the OpenMath CDs of the
 "MathML Compatibility Group" as a basis for the  CMathML3 set. And the CD
 fns1 contained left/right_inverse . By the OpenMath CD rules, we cannot
 just drop symbols from a CD or backwards compatibility reasons.
 Therefore we would have to invent a new CD (e.g. fns3). We will have to
 discuss how to do this.

 >And what is 'right_compose' ???

 This could be added from what I understand the rules to be.

 >I have never thought of 'lambda' as anything to do with maths, >which
 managed for 500 years of specifying functions without it.

 The existence of 'lambda' is probably a testimony of who was in the
 OpenMath and MathML groups at the time the fragments were made. But
 'lambda' was in both in OM2 and MathML2, so we should leave it there.
 Also it is part of 'modern math' in my view. I teach it in K-14 (i.e.
 first-semester discrete math). Finally it is a good representational
 concept for integrals and such.

-- 
Ticket URL: <https://trac.kwarc.info/OM3/ticket/43#comment:3>
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