[Trac] [OpenMath] #42: CD arith1

[OpenMath]

#42: CD arith1
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    Reporter:  jauecker    |           Owner:  kohlhase  
        Type:  proposal    |          Status:  new       
    Priority:  major       |       Milestone:  CD3 Draft1
   Component:  CD3 Format  |         Version:            
    Keywords:              |   Include_gantt:  0         
Dependencies:              |      Due_assign:  YYYY/MM/DD
   Due_close:  YYYY/MM/DD  |  
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 More description, which should be (mathematically) both as informal as
 possible and as formal as necessary, is needed of such phrases as
 'arithmetic functions'.  We cannot assume (even in the K-12 world)
 that such phrases 'mean the same to everyone'; and if we are making
 that assumption then it should be very easy to explain, with only
 minimal formality, what this 'common understanding' is.

 This appears a few times: 'The argument should be numerically valued.'
 Meaning what exactly?  Distinct from 'must be a number?'
 And why does it not appear for all arithmetic things?

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 Are the following supposed to be distinct mathematical concepts?
 If so, how do I know which should be used?

 This operator is used to construct
 an expression which represents
 the ...

 This operator is used to construct
 the ...

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 Descriptions like the one below are very useful for 'knowledgeable
 mathematicians who work with mathematical software'; but is that our
 only audience?
 [In this particular case <plus/>, I would restrict it
 to the (mathematically) associative operation on mathematical numbers
 (not numbers in computers). Note also that 'multiplication' comes with
 no such detailed description,right or wrong!]

 If no operands are provided, the expression represents the
 additive identity.  If one operand, a, is provided the expression
 evaluates to "a". If two or more operands are provided, the expression
 represents the (semi) group element corresponding to a left
 associative binary pairing of the operands. The meaning of mixed
 operand types not covered by the signatures shown here are left up to
 the target system.

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 'the symbol representing ...'  should probably be 'this symbol
 represents ...', otherwise we are implying that there is no other way to
 'represent ...'.

 Such phrases are sometimes followed by 'the ...' but sometimes by 'a/an
 ...'.
 Both are somewhat misleading but using all two of them suggests a
 non-existent distinction.

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 What is 'right-division' doing in a description for K-12 maths?
 [Not the only problem with <divide/>.]

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 The following may or may not include the case 'when the 2nd argument
 is a matrix': 'when the second argument is not an integer ...'

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 Are the terms 'function' and 'expression' and 'argument' interchangeable?

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

 Apart from their historical provenance, why should the descriptions of
 <sum/> and <product/> look totally different from those for the
 <big_*/>s.

-- 
Ticket URL: <https://trac.kwarc.info/OM3/ticket/42>
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