Re: Galileo's Paradox

On Wed, 29 Nov 2006 17:12:04 +0000 (UTC), stephen@xxxxxxxxxx wrote:

Six wrote:

[. . .]

You suggested I conduct my argument without using the term
'infinity'. I am quite happy to do that. I suggest you conduct the rest of
your argument without using the term 'cardinality'.

Why? Cardinality has a definition in set theory.

The issue is whether "cardinality" has a definition in mathematics not
set theory unless you're suggesting set theory is all of mathematics.

'infinity' does not have
a definition.

Sure it does. In mathematics "infinity" is the "number of
infinitesimals". Once again, Stephen, you seem to be confusing
mathematics with set "theory" which isn't really even a theory at all
because it can't be demonstrated true but merely represents a series
of analytical techniques applied to sets which certainly don't
encompass all of mathematics.

Do you really think that the two words are on an equal footing?

Actually not because "infinity" a well defined mathematical concept
whereas "cardinality" is only an ambiguously defined concept
mathematically restricted to undemonstrable set analytical techniques.

~v~~
.

Relevant Pages

  • Re: An uncountable countable set
    ... in so far as cardinality can be said to be a "measure" of an infinite set. ... Whether comparison of sets in terms of cardinality meets the criteria associated with some notion of "measurement" can of course be questioned, but has pretty much nothing to do with modern set theory. ... If set theory is a generalization of all mathematics, then none of the general conclusions it draws should be at odds with any of the specific conclusions drawn throughout mathematics. ...
    (sci.math)
  • Re: Why does everyone do it?
    ... applied to mathematics. ... There are all sorts in sci.math who argue against set theory. ... When it comes to uncountable ordinals, say those of cardinality aleph_1, ...
    (sci.math)
  • Re: An uncountable countable set
    ... is the subject and not things such as x to which cardinality applies. ... equinumerosity of x which relies on the cardinality of x. ... So this means we couldn't do exactly what without set theory? ... I ask once more is why does anyone need set theory to do mathematics? ...
    (sci.math)
  • Re: Cantor Confusion
    ... >> Well, in mathematics the first form is valid, the second is not valid. ... > If actual infinity is assumed to exist, then the second case is valid. ... kann also omega sowohl als eine gerade, ... Set theory is more basic than analysis. ...
    (sci.math)
  • Re: Cantor Confusion
    ... denote potential or actual infinity. ... Meanwhile I see mounting evidence for my suspicion that set theory is ... It claims to rule continuity and ... Cantor's indeed naive fabrication of cardinality, ...
    (sci.math)