Re: Cantorian pseudomathematics

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

P(arbitrary natural) = [1/n -> 0 as n -> oo] 

That makes no particular sense.  The probability P(arbitrary natural)
is a number, right?  A number in [0,1], right?  I don't know what that
thing on the right is.  Is it a number?  If so, which one?
Zero perhaps or something else?
Did you mean:
  P({k}) = lim_{n->oo} 1/n
so P({k}) = 0?  If so, why not write P(arbitrary natural) = 0?


You are right, of course, but I'm trying to communicate with Virgil
in his own parlance.


Okay, let me see if I understand you correctly.

* There is a uniform distribution P on N.

* This distribution assigns P( {k} ) = 0 for every k in N. 

You threw away the additional information here: P( {k} ) = 1/n -> 0 .

* Probability distributions satisfy countable additivity.

Is this a correct summary of your views? 

Countable additivity is satisfied only if N = (1..n) _and_ P( {k} )
as defined above by me, are considered _together_. You can't fool me
(or Jaynes) by first concluding that P( {k} ) = 0 and _then_ consider
additivity over (1 .. n -> oo) . This is just foul play with limits,
as every first year (calculus) student can tell you.

Han de Bruijn

.

Relevant Pages

  • Re: Planets and Stars - an idea
    ... the average or below-average student, ... in my old calculus textbook there was some extra vector calculus stuff which we didn't cover in class which studied the behavior of curves. ... Different from answering in an extra clever way that makes the teacher do extra work. ...
    (rec.arts.sf.science)
  • Oh my god, another RSTs ignorant statement "No Qing Dynasty sent any student to foreign country"! I
    ... another RST's ignorant statement "No Qing Dynasty sent any ... student to foreign country"! ... Hey, Rusty old fool, read the following and stop being stupid!!! ...
    (soc.culture.china)
  • Re: How not to teach mathematics
    ... the illusion to the student of achievement rather than learning. ... skills before they could take courses in the regular Math curriculum. ... Some of the students had actully Taken "Calculus " but had all aken at laest ...
    (sci.math)
  • Re: off topic: Ubuntu gets some bad publicity
    ... Most of the larger ISPs, cable or dsl, provide proprietary software and ... Of course it's all bull, ... student. ... When I took calculus, the teacher made us aware we needed graphing ...
    (comp.os.linux.misc)
  • Re: Public School was a waste of my time (Re: When even a Republican can see it....)
    ... Sounds awful, but maybe if I'd had that, I'd know some calculus now. ... I was an A student in math classes until I hit calculus. ... transformations after the fact, but as to the question of why those ... That is, they have a list of prerequisites, but all too ...
    (rec.arts.sf.fandom)