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To: lojban
Subject: Re: [lojban] 2 maths questions
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From: Thorild Selen
John Cowan writes:
> On Wed, 5 Jul 2000, And Rosta wrote:
> > but how does one express the notion that the latter is bigger, because
> > there are twice as many integers as even numbers? In what property
> > does the set of integers exceed the set of even numbers? [...]
>
> I was just wondering about this myself the other day. If there is an
> answer, it certainly is not commonly taught. [...]
Aren't you trying to make things a little too complicated here?
What you really want to say is probably that the set of even
numbers is a _proper subset_ of the set of integers, so there
is certainly a well known name for this relation.
Naming the property in which one of the sets exceeds the other may
be a bit trickier. Maybe one could call it "the property of containing
much" (that sounds like size, but, as John said, the two sets are of
the same size, so we can't call the property "size" unless we really
want to cause confusion). The relations "larger" and "smaller" on
this property should be the superset and subset relations (thus
not a total ordering).
Using a "frequency" property to compare these sets was also mentioned.
The idea is probably that the the number of integers in the range
[0,n] that are in the first set is larger than the number of integers
within the same interval that are in the second set, and that this
holds for arbitrarily large values of n. I can't come up with a better
name for this property, but if you need to talk about it, it would
probably be wise to start by declaring a name for it.
/Thorild