Re: New approach to annex D of the 754-R proposal.

[Nick Maclaren <nmm1@xxxxxxxxxxxxx>]

Peter Henderson <petercbh@xxxxxxxxxxx> wrote:
> In addition to the behaviour you describe below, I would like to propose 
> the following:
>
> If f(x1, .. xN) diverges, but does not tend to +infinity or -infinity,  
> as (x1, ... xN) tends to (X1,...,XN), then f(X1,...,XN) should return an 
> infinity.  Here by diverge, I mean for all M, |f(x1,...,xN)| > M for all 
> (x1,...,xN) sufficiently close to (X1,...,XN).  The choice of sign 
> should follow the same principles used to choose the sign when the limit 
> is 0.
>
> The type of behaviour this rule is designed to cover is that of 1/(x-1) 
> as x tends to 1, or 1/(x*sin(1/x)) as x tends to 0.

Yer whaa?

Would you like to explain what the values of the following are and,
most of all, why, for x = -0 and x = +0?

1/(x*sin(1/x))
1/(x^2*sin(1/x))
1/(x*sin(1/x^2))
1/(x*sin(-1/x))
1/(x^2*sin(-1/x))
1/(x*sin(-1/x^2))

I posted a semi-mathematical rule that had the merits of being
mathematically consistent and obeying the principle of least
surprise, which would make those NaNs.  Now, I know why that is
politically unacceptable, but you do need to justify that your
'rule' is at least well-defined.

As I don't know of any well-defined principles used to choose signs
when the limit is 0, and there CERTAINLY aren't any specified to
any precision, your rule doesn't look meaningful.


Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email:  nmm1@xxxxxxxxx
Tel.:  +44 1223 334761    Fax:  +44 1223 334679