Re: Distinct linear orderings on Z

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 10:26:21 -0500

Jesse F. Hughes said:
> Tony Orlow (aeo6) <aeo6@cornell.edu> writes:
>
> > Jesse F. Hughes said:
> >> Tony Orlow (aeo6) <aeo6@cornell.edu> writes:
> >>
> >> >> Can you arrange these sets in order of "number of elements"?
> >> >>
> >> >> (a) the set of of multiples of 1000,
> >> > f(x) = 1000*x => |f(x)| = |N|/1000
> >> >> (b) the set of squares,
> >> > f(x) = x^2 => |f(x)| = sqrt(|N|)
> >> >> (c) the set of primes.
> >> > hard problem but...
> >> > f(x)~=1/ln(x) => ln(|N|)
> >> >
> >> > Therefore |c|<|b|<|a| in my book.
> >>
> >> What is the definition of |x| that supports these "calculations"?
> >>
> >>
> > That notation is supposed to denote the cardinality of the set x.
>
Doh! (bangs head on rock) NOT cardinality. oops! Size of the set by my
thinking....let's call it bigulosity. The bigulosity of the set X shall
henceforth be denoted by !@#(X). What I meant to say was:
!@#(c) < !@#(b) < !@#(a)

> Obviously not. Cardinality is well-defined and supports none of
> those claims. In terms of cardinality, it is utterly, stupefyingly
> clear that |a| = |b| = |c|.
>
> Dave had given you an out by using the vague term "number of
> elements", but your response says that you meant the well-defined term
> "cardinality". Clearly, then, your answers are just wrong.
>
> (There is also no definition of division, square root or logs of
> arbitrary cardinalities, so your answers are worse than wrong. The
> "calculations" that lead to the inequalities are literally
> meaningless.)
Ah, but that is not true of bigulosities. In bigulosities one can define
relative levels of infinity using mapping functions and derivatives thereof,
for a fine granularity of values. :)
>
> 

-- 
Smiles,
Tony

Relevant Pages

  • Re: Distinct linear orderings on Z
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  • Re: Distinct linear orderings on Z
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