CD arith1

[jbs1]

migrated from Trac, where originally posted by jauecker on 3-Sep-2008 11:29am

Chris:

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 , 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 .]

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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?

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

[jbs1]

migrated from Trac, where originally posted by jhd on 3-Sep-2008 4:32pm

Replying to [ticket:42 jauecker]:

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? Actually, I only saw it once in arith1, on 'abs'.

I suspect that the original intent was meant to distinguish operators like abs from a purely algebraic operation, which can be applied to indeterminates. But it is probably meaningless in practice.

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 ... I believe they are identical

James

[jbs1]

migrated from Trac, where originally posted by clange on 13-Sep-2008 1:34am

Jakob, here are my ideas about copying the discussion to the wiki – Thanks! (Additional comments that cannot easily be put into practice are in italics as a to-do for my own modelling of the argumentation ontology; you can ignore them for copying.)

Let me divide the comments along the lines:

"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.

Issue with the CD.

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?

Another issue with the whole CD, I think it's just too much work to put it to every affected symbol, and it's rather about a general policy.

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 ... 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 , 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 ...

I'd file it as an Issue separately for each symbol where it is applicable.

'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.

I'd file (a copy of) this as an Issue with any symbol where it occurs.

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

Issue with divide.

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

Issue where it occurs.

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

That sounds pretty general again, so I'd say: Issue about the CD.

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

I'd file this as an Issue once for "sum" and once for "product". Still, I don't really understand what the "big" symbols are referring to, as there is no "big_sum" nor a "bigproduct." So I'd suggest that for each of those two issues, you post a plain reply asking "What is big...?"

[jbs1]

migrated from Trac, where originally posted by jauecker on 4-Nov-2008 11:07pm

There is an alternative version of this discussion at http://wiki.openmath.org/?title=cd%3Aarith1 where it is directly linked to the CD, and where you can also discuss about individual symbols and even Properties and Examples. Please consider registering there.