Re: One to One Correspondence

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 03/27/05 

Date: Sun, 27 Mar 2005 06:57:39 -0600

On Sat, 26 Mar 2005 17:00:00 -0500, "Sanford Geraci"
<sageraci@hotmail.com> wrote:

>Since you can show a n:1 (n not equal to 1) correspondence between the set
>of Natural Numbers and the set of Even Natural numbers, why is it that the
>1:1 correspondece wins?

[guessing what we mean by this:]

Because the _definition_ says something about "there exists a 1-1
correspondence", not "there does not exist an n-1 correspondence".

Next question: why does the definition say that?
A: No reason, it's just a definition. The concept defined by that
definition turns out to be interesting.
Q: Why is it more interesting than the other definition?
A: No accounting for tastes. If you like the other definition
better go ahead and think about what it entails. (But make certain
to be clear about the fact that you're talking about a _different_
concept.)

************************

David C. Ullrich

Relevant Pages

  • Re: Rounding currency.
    ... I can't see what your formula actually does, but guessing at it, does this ... HTH, ... Please keep all correspondence within the Group, ... Prev by Date: ...
    (microsoft.public.excel.worksheet.functions)
  • Re: What is the cell data reference for 5th row and 7th column called
    ... I'm guessing, ... Regards, ... Please keep all correspondence within the NewsGroup, ...
    (microsoft.public.excel.newusers)
  • Re: Cantors proof that #(Evens) = #(Naturals) is inconsistent
    ... David Ferguson, PAY ATTENTION to the following two paragraphs since you ... If A and B are nonempty finite sets, and there is a 2-to-1 correspondence ... that the cardinality of E* is two times the cardinality of E, ... >> say that this is not a bijection. ...
    (sci.math)
  • Re: What are the odds of guessing a number between 1 and 20 digits long?
    ... David C. Ullrich wrote: ... between 1 and 20 digits then your chance of guessing ... social security number, for example, which is nine digits long. ...
    (sci.math)
  • Re: colums
    ... Check out this page of David McRitchie's: ... Please keep all correspondence within the NewsGroup, ... "Kingdom" wrote in message ...
    (microsoft.public.excel)