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Continuing issues with self-reference
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Jack
May 24, 2013, 11:11:07 AM5/24/13
to
When I was still learning the ropes (even more than I am now), I would write
things like 'Let x be y for which....' and Paul would reply with 'STOP
THAT'. It took me a while to realise what his objection was all about (I
still don't think I quite get it, because my version was much briefer than
saying something like 'Let x be the real number for which...', so in view of
the fact that my y could *only* be a real number, given what followed, I
assume it's purely a stylistic matter).
Now I think I have hit upon exactly the what the mindset was that made me
write it in that way. I have got this definition that, currently, goes:
'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
Note that the inserted 'unique' is not strictly necessary in the definition,
but I use it to help the reader and to make the ensuing assertions.
In view of Paul's objections I don't know whether I ought to write it as
'Let n(j, g) be the unique element of I for which m(j, n(j, g)) = 1'
or whether this amounts to unacceptable/undesirable self-reference, and
whether the insertion of 'unique' makes a difference. (Certainly I have been
advised that it's OK to say 'Let r be the lowest x for which...'.) And maybe
I should remove 'unique'?
What say ye?
With thatnks in advance.
things like 'Let x be y for which....' and Paul would reply with 'STOP
THAT'. It took me a while to realise what his objection was all about (I
still don't think I quite get it, because my version was much briefer than
saying something like 'Let x be the real number for which...', so in view of
the fact that my y could *only* be a real number, given what followed, I
assume it's purely a stylistic matter).
Now I think I have hit upon exactly the what the mindset was that made me
write it in that way. I have got this definition that, currently, goes:
'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
Note that the inserted 'unique' is not strictly necessary in the definition,
but I use it to help the reader and to make the ensuing assertions.
In view of Paul's objections I don't know whether I ought to write it as
'Let n(j, g) be the unique element of I for which m(j, n(j, g)) = 1'
or whether this amounts to unacceptable/undesirable self-reference, and
whether the insertion of 'unique' makes a difference. (Certainly I have been
advised that it's OK to say 'Let r be the lowest x for which...'.) And maybe
I should remove 'unique'?
What say ye?
With thatnks in advance.
William Elliot
May 24, 2013, 9:39:19 PM5/24/13
to
> I have got this definition that, currently, goes:
> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
What's n(), I and m()?
> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
> Note that the inserted 'unique' is not strictly necessary in the definition,
> but I use it to help the reader and to make the ensuing assertions.
a comment immediately after the definition.
> What say ye?
Gee whiz, you expect to much of us - to rememeber all your stuff. Cut the
blah, blan, be precise with your question going directly to defining your
special notations and presenting your question.
Jack
May 25, 2013, 9:36:33 AM5/25/13
to
"William Elliot" <ma...@panix.com> wrote in message
news:Pine.NEB.4.64.13...@panix3.panix.com...
>> I have got this definition that, currently, goes:
>> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
>
> What's n(), I and m()?
Why should it matter? My query concerns the structure of definitions
>> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
>
> What's n(), I and m()?
vis-a-vis self-reference.
Is there anything objectionable about saying 'Let f(x) be
k in <some set concerning x> for which <such-and-such to do with k is
true>'? Or should f(x) take the place of k throughout?
Peter Percival
May 25, 2013, 10:45:13 AM5/25/13
to
Jack wrote:
> When I was still learning the ropes (even more than I am now), I would write
> things like 'Let x be y for which....' and Paul would reply with 'STOP
> THAT'. It took me a while to realise what his objection was all about (I
> still don't think I quite get it, because my version was much briefer than
> saying something like 'Let x be the real number for which...', so in view of
> the fact that my y could *only* be a real number, given what followed, I
> assume it's purely a stylistic matter).
>
> Now I think I have hit upon exactly the what the mindset was that made me
> write it in that way. I have got this definition that, currently, goes:
> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
If it is unique, that's fine. Indeed, neither
> When I was still learning the ropes (even more than I am now), I would write
> things like 'Let x be y for which....' and Paul would reply with 'STOP
> THAT'. It took me a while to realise what his objection was all about (I
> still don't think I quite get it, because my version was much briefer than
> saying something like 'Let x be the real number for which...', so in view of
> the fact that my y could *only* be a real number, given what followed, I
> assume it's purely a stylistic matter).
>
> Now I think I have hit upon exactly the what the mindset was that made me
> write it in that way. I have got this definition that, currently, goes:
> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
Let n(j, g) be the k in I for which m(j, k) = 1
nor
Let n(j, g) be k in I for which m(j, k) = 1
would define n(j, g) if k weren't unique.
> Note that the inserted 'unique' is not strictly necessary in the definition,
> but I use it to help the reader and to make the ensuing assertions.
> In view of Paul's objections I don't know whether I ought to write it as
> 'Let n(j, g) be the unique element of I for which m(j, n(j, g)) = 1'
> or whether this amounts to unacceptable/undesirable self-reference, and
> whether the insertion of 'unique' makes a difference. (Certainly I have been
> advised that it's OK to say 'Let r be the lowest x for which...'.) And maybe
> I should remove 'unique'?
>
> What say ye?
> With thatnks in advance.
>
>
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne
Jack
May 25, 2013, 11:05:03 AM5/25/13
to
"Peter Percival" <peterxp...@hotmail.com> wrote in message
news:knqipq$m1o$1...@news.albasani.net...
> Jack wrote:
>> When I was still learning the ropes (even more than I am now), I would
>> write
>> things like 'Let x be y for which....' and Paul would reply with 'STOP
>> THAT'. It took me a while to realise what his objection was all about (I
>> still don't think I quite get it, because my version was much briefer
>> than
>> saying something like 'Let x be the real number for which...', so in view
>> of
>> the fact that my y could *only* be a real number, given what followed, I
>> assume it's purely a stylistic matter).
>>
>> Now I think I have hit upon exactly the what the mindset was that made me
>> write it in that way. I have got this definition that, currently, goes:
>> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
>
> If it is unique, that's fine.
So I imagine it's the reference to the set I that distinguishes this case
>> When I was still learning the ropes (even more than I am now), I would
>> write
>> things like 'Let x be y for which....' and Paul would reply with 'STOP
>> THAT'. It took me a while to realise what his objection was all about (I
>> still don't think I quite get it, because my version was much briefer
>> than
>> saying something like 'Let x be the real number for which...', so in view
>> of
>> the fact that my y could *only* be a real number, given what followed, I
>> assume it's purely a stylistic matter).
>>
>> Now I think I have hit upon exactly the what the mindset was that made me
>> write it in that way. I have got this definition that, currently, goes:
>> 'Let n(j, g) be the unique k in I for which m(j, k) = 1'.
>
> If it is unique, that's fine.
from the one Paul was objecting to...?
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