Re: Proposal: 6NF

Quoth "Keith H Duggar" <duggar_at_alum.mit.edu>:
> vc wrote:
>> Marshall wrote:
>> > I do not recall learning anything in secondary school
>> > which would suggest 2 and 2.0 were numerically different
>> > in any way. Nor can I think of any *arithmetic* way to
>> > distinguish between 2 and 2.0.
>>
>> You have to construct all the real numbers and prove that
>> 2 is an element of the set.
>
> Any mathematical number construct that fails to equate 2.0
> and 2, fails to model our most basic common sense or
> "elemntary school" concept of the number 2.

In abstract algebra, you get groups and other structures where 2 may be a meaningful value, but 2.0 isn't, because there isn't any inherent notion of fractional values. Indeed, in the realm of discrete mathematics, it's unmeaningful (even undesirable!) to have any values lying between 1 and 2 and 2 and 3.

Proof by induction, for instance, depends on the notion that there are no intermediate values.

I don't think that "elemntary school" concepts are of any particular relevance when looking at mathematical structures; they are what they are, irrespective of whether a layman can relate them to anything that seems familiar to the layman.

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