```Date: Sun, 26 Oct 2003 00:31:55 +0100 Reply-To: John Whittington Sender: "SAS(r) Discussion" From: John Whittington Subject: Re: Rounding and Prefixing and Suffixing Observations Comments: To: Ian Whitlock In-Reply-To: Content-Type: text/plain; charset="us-ascii"; format=flowed 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 ---------------------------------------------------------------- Dr John Whittington, Voice: +44 (0) 1296 730225 Mediscience Services Fax: +44 (0) 1296 738893 Twyford Manor, Twyford, E-mail: John.W@mediscience.co.uk Buckingham MK18 4EL, UK mediscience@compuserve.com ---------------------------------------------------------------- ```

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