Pat Hayes wrote:
> On Sep 29, 2009, at 10:30 PM, Joe Collins wrote:
>> > Well, actually, it is. It means 'the same as'. It does not mean 'nearly
>> > the same as' or 'not the same as, but so close that I can't measure the
>> > difference' or 'very likely very close to' or any of these other
>> > notions. Equal means *equal*. If A=B then there is *one thing* with two
>> > names, not two things that are very close.
>> You are correct in that approximately equal, not being transitive, can
>> not be an equivalence relation.
>> In that case, I must conclude that
>> > 1 m = 1.00 m : true or false?
>> is false
> ?? I am gobsmacked, both by the conclusion and by the logic. Why is 1
> only approximately equal to 1.00 ? The bare numeral '1' refers to the
> number one. The decimal numeral '1.00' refers to the sum of the number
> one, zero tenths and zero hundreths. I believe if you do the addition,
> that also comes to one.
To quote again from the SI standard, ISO/DIS 80000-1, "Quantities and units"
7.3.3 Error and uncertainty
When a number is given without any further information it is generally
interpreted so that the last digit is rounded with a rounding interval equal to
1 in the last digit (see Annex B). Thus, for example, the number 401 008 is
generally assumed to represent a value between the two values 401 008,0 ± 0,5,
i.e. between 401 007,5 and 401 008,5.
Not a hallucination, just reading the standard I thought we were trying to
capture (which, being educated as a physicist, I already knew before reading
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
Washington, DC 20375
(202) 767-1122 (fax)
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