Re: [Phys-l] singular limits

[Brian Whatcott <betwys1@sbcglobal.net>]

I feared the worst when I started reading John D
on zeroes.
For a mathematician, a zero is rather well defined.
And John D displays extended mathematical grasp.
So...it would be easy to imagine that he would say:
of course a  zero is a zero.

But  yes indeed: for physical units, the unit of measure figures
in the result: ANY result.
(This same line of reasoning applies when a blogger starts
working numbers concerning domestic radiation sources.
The zero of distance rightly applies to any source under
comparision: NOT a point source estimate for the cell phone,
and a surface source estimate for the microwave.
Apples: oranges,   and all that....)

Brian W

.

John Denker wrote:
> 0 newtons is also equal to 0 furlongs.
> This applies to vector character as well as to
> dimensions and units:
>
>            0 newtons in the Xhat direction 
>          = 0 newtons in the Yhat direction
>          = 0 cubits in the Zhat direction
>
> HOWEVER ... this is an example of a singular limit./snip/
> In particular, physics is one of the natural sciences,
> which means it is not an exact science in the sense that
> arithmetic is exact.  So even though Q(m) is false when m 
> is exactly zero, it is true when m is _approximately_ zero.