Re: Orlow cardinality question

Tony Orlow wrote:
> In my College Achievement Tests, I
> scored an 800 out of 800 in math, and above 700 on three other
> Achievement tests.

So we understand you believe that your skill in mathematics matches
your confidence. Could you just clarify whether you believe that
basically the entire system of maths education of the modern world has
got it wrong, and you have uniquely identified the flaw. Or do you
believe that the many people here who have told you that the set of
finite integers (pofnats) is finite are misinformed - in which case
could you perhaps point to a textbook or university prof's webpage that
confirms your (mis)understanding?


> Let me reiterate. The set is infinite. There is a constant finite
> difference between any two successive members. Therefore the set
> contains infinite values.

"Therefore"? No-one seems to accept this "therefore" except you.
Consider the sequence of partial sums of sigma(n=0,oo)(1), viz: 1, 2,
3, 4, 5, ...

Your argument about "constant finite difference" implies that this
sequence diverges (in careful mathspeak) or "equals infinity" in
sloppyese. No-one disagrees. There is plainly no finite limit (in
either the technical or non-technical sense) to this sequence of finite
values. If you believed that somehow the limit must always be a member
of the set, then again you would have shown the odd situation that a
set of elements with a particular property (being a pofnat) included at
least one element that didn't. But if you don't believe that the limit
must be an element of the sequence, where on earth do these "infinite"
members come from?

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: infinity
    ... > One has to start with a stadard infinite range in common, ... sequence that never ends as a sequence with an end "at infinity". ... Tinfinite sets of even naturals - what real mathematicians mean by "the ... includes members which aren't members, ...
    (sci.math)
  • Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]
    ... Orlow again conflates the finiteness of a sequence or series ... >>> with the finiteness of its members. ... >> difference between the naturals, which is not true of the reals. ... you can't squeeze an infinite number of them in a finite interval. ...
    (sci.math)
  • Re: No Unique Initial Segment And No Characteristic Expansion
    ... So how did you conclude the sequence is original? ... Infinite people all toss coins infinite times each. ... CHARACTERISTIC EXPANSION to distinguish it from members of the list. ...
    (sci.logic)
  • Re: Orlow cardinality question
    ... > Tony Orlow wrote: ... The set is infinite. ... >> difference between any two successive members. ... > either the technical or non-technical sense) to this sequence of finite ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... ....2222, they are actually infinitely distant elements of a sequence, ... smallest positive number, on the infinite scale. ... That's the ordering used by Cantor to prove their countability. ... If a set S is countable, then there is a total order < of S such that ...
    (sci.math)