Date: Sun, 26 Oct 2003 00:31:55 +0100
Reply-To: John Whittington <John.W@MEDISCIENCE.CO.UK>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: John Whittington <John.W@MEDISCIENCE.CO.UK>
Subject: Re: Rounding and Prefixing and Suffixing Observations
In-Reply-To: <DE7408C714122F4BB5221C1E73A135D10E1C03@remailw2k2.westat.c om>
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At 11:32 25/10/03 -0400, Ian Whitlock wrote:
>John,
>In the light of Saturday morning :~) I would have to say 0 and 0.000 are
>different. One has a single digit and one has 4 digits and a decimal point,
>hence they *are* different, not *may be* different.
I can't argue with that, and never intended to! Your original comment was
not that they 'were different', but that they 'were different
representations' (of the same number). This is at risk of getting very
semantic, although I do think there are some serious and important
underlying points (i.e. causes of possible confusion or misunderstanding).
As I said before, I certainly do not deny that 0 and 0.000 MAY/CAN be
'different representations of the same number'. However, I think it also
clear that they may/can be representations of different numbers. For
example, in the absence of any further information, 0 might be a
representation of 0.49, whereas 0.000 might be a representation of
0.0004999 - clearly two very different numbers.
>I don't understand your argument about 0.499. If 0.000 does not represent
>the number 0, then to me it conveys the extra information about a number
>that I cannot know precisely, i.e. that the first three decimal digits must
>be 0 and the fourth digit cannot be larger than 4. So the real number (not
>representation) 0.00049999 would be included in the representation 0.000
>while the real number (not representation) 0.0005 would not.
Exactly. Even if it is not explicitly formulated as a 'rule', I think that
is the implied convention. To me, trailing zeros (after a decimal point)
carry implied information about the precision and/or rounding. In other
words, if a value is represented as 0.0000, I take that to mean that the
true value is not equal to or greater than 0.0005 - and also not equal to
or less than (or should that just be 'less than'?) than -0.0005.
>Part of the problem in talking about these things is the standard practice
>to confuse the object with representation of the object. Now 0.000 can
>represent both a number, and that number is 0, and an idea about the size of
>a measurement, which was explicated above.
Indeed. In fact, I think that's almost the _entirity_ of the
problem. However (and maybe some will disagree), as I've said, my belief
is that trailing zeros (after a decimal point) in the representation of a
number are conventionally used to imply things about precision.
Kind Regards
John
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