I’m always impressed with the quality of answers that come out of these 
discussions - inevitably I’m reminded that dispatching off the right parties is 
ultimately where the power lies (when you cheat - it always seems to end up 
with a gotcha).

Thanks guys.

Tim

> On 23 Mar 2020, at 15:15, James Foster <smallt...@jgfoster.net> wrote:
> 
> 
>> On Mar 23, 2020, at 8:14 AM, Sven Van Caekenberghe <s...@stfx.eu> wrote:
>> 
>> Both are excellent suggestions.
>> 
>> We have to think a bit about the consequences.
>> 
>> Still, both would not solve the problem of what to return when the 
>> collection is empty.
> 
> Zero?
> 
>> 
>>> On 23 Mar 2020, at 15:47, Konrad Hinsen <konrad.hin...@fastmail.net> wrote:
>>> 
>>> Am 23.03.20 um 14:45 schrieb James Foster:
>>> 
>>>>> On Mar 23, 2020, at 6:06 AM, Sven Van Caekenberghe <s...@stfx.eu> wrote:
>>>>> 
>>>>> What you found out now is that the clever trick used to avoid picking an 
>>>>> additive identity (picking an element, counting it twice and then 
>>>>> subtracting it) leads to a loss of precision when floating point numbers 
>>>>> are involved. This is an important issue.
>>>> If this approach is to be preserved, then each class should have an 
>>>> additive identity so instead of adding and subtracting an object, we let 
>>>> the object tell us its zero.
>>> 
>>> Or define a singleton class "Zero" with a + method that returns the other 
>>> operand, and use that Zero object for the additive identity.
>>> 
>>> Konrad.
>>> 
>>> 
>> 
>> 
>> 
> 
> 


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