Re: infinity

Tony Orlow wrote: 
William Hughes said:

Tony Orlow wrote:

David R Tribble said:

Tony Orlow wrote:

The range as maximum possible difference cannot be specified
without specification of the bounds of the set, but in any case, the maximum
possible difference is not infinite if no differences can possibly be
infinite.


Can the maximum possible difference be unbounded if the differences
between any members are unbounded?



I would say so, yes. The range of the finite naturals is an unboundedly large
finite value.


The problem is that no natural number is unboundedly large.
(Except for a sour natural number of course.) So the range
of the finite naturals is not a natural number.

                           -William Hughes



For any given n in N, the value range in the set of naturals from 0 to n is n, so how can the range NOT be a natural number. The problem is that we cannot name any such largest finite. You say it doesn't exist. I say the range must exist where there are valures, but if we have no maximal value, then we have no maximal difference, and cannot identify the range, except to say it is unboundedly large, but finite.

If there is, as you state, no maximal difference, and if, as you have also stated, the value range is defined as the maximal difference, then it would seem to follow that there is no value range. Yet you deny this conclusion. Why?

Matt
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... > Tony Orlow wrote: ... > But this list is only a countably infinite number of reals. ... it lists only binary fractions with a finite number ... > the infinite set of all finite naturals. ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >> possible infinite difference between finite values. ... And then emended it to say that the range of such an open set is "<1", ... > but that a set of naturals can't. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Then I say there are infinitely many naturals. ... this an infinite set, ... That identity relationship characterizes all the initial finite subsets ...
    (sci.math)
  • Re: Orlow cardinality question
    ... Tony Orlow wrote: ... > distinct finite naturals, and have pointed out the flaw in the one proof you ... if the set of natural numbers is infinite, ... you give a proof then people don't argue with you, ...
    (sci.math)
  • Re: infinity
    ... >> Tony Orlow says... ... Good way to kludge away the largest finite. ... And of course aleph_0 is just such an infinite n ... so we only have finite naturals. ...
    (sci.math)