From jjllambias@hotmail.com Fri Jul 07 16:54:18 2000
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To: lojban@egroups.com
Subject: RE: [lojban] 2 maths questions
Date: Fri, 07 Jul 2000 16:54:14 PDT
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From: "Jorge Llambias"
la and cusku di'e
> > >but how does one express the notion that the latter is bigger, because
> > >there are twice as many integers as even numbers?
> >
> > That erroneous notion can be expressed, for example, as:
> >
> > lei relmeina'u lei kacna'u cu xadba le ka kaclai
> > The even numbers are half the integers in number.
>
>Did you realize that I am trying to formulate a statement that is both
>true and expresses this idea?
If you want to make a mathematical statement, the idea is
just wrong, there are not twice as many integers as even
numbers in the usual mathematical sense. It is of course
possible to define some new mathematical function that
assigns to the integers twice the value that it assigns
the even numbers (the function proposed taking limits is
probably the best), but what do we want it for?
> > lei kacna'u lei relmeina'u cu zmadu le ka denmi
>
>Is "denmi" sufficient?
It has been pointed out that "dense" is already used for
something else in maths. For example, the set of rationals
is dense in the set of reals. Even though an interval of
rationals is full of holes, any real interval contains
rationals. The integers are not dense because you can find
intervals where there are no integers (for example between
0.2 and 0.5).
{denmi} does not necessarily mean this yet, but it is
reasonable to expect that Lojbanist mathematicians will
want to use it with that sense.
>Is denmi in the appropriate part of number space a
>mathematically sensical notion?
Not until someone defines it. But then why not?
>Can one analogously express the frequency
>of trains as denmi in time?
It seems possible. x3 would have to be the time interval.
co'o mi'e xorxes
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