Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

stephen_at_nomail.com
Date: 11/19/04 

Date: 19 Nov 2004 18:27:04 GMT

In sci.math Eray Ozkural exa <examachine@gmail.com> wrote:
: We use the concept of bijection to reason about the equivalence of the
: "sizes" of supposedly infinite sets, like natural numbers. Under the
: axioms of ZFC, we can comfortably talk about a bijection between even
: and odd numbers, and even numbers and all natural numbers. However,
: this would fail if we were to give the "subset" account of comparing
: the magnitudes or sizes of supposedly infinite sets. Which one is
: correct?

That is a meaningless question. Two sets have the same cardinality
if there exists a bijection between them. That is the definition.
How can you claim that the definition is not correct?

If we defined "same cardinality" differently then of course
sets that had the same cardinality under the old definition
might no longer have the same cardinality under the new definition.
No surprise there. The only interesting question is which
definitions are more useful.

Like so many of the people who seem to object to Cantor's
proof, you are apparently arguing with the definitions used in the
proof, not the proof itself.

Stephen

Relevant Pages

  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... :> In sci.math Eray Ozkural exa wrote: ... :>: We use the concept of bijection to reason about the equivalence of the ... :>: "sizes" of supposedly infinite sets, ... Two sets have the same cardinality ...
    (comp.theory)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... :> In sci.math Eray Ozkural exa wrote: ... :>: We use the concept of bijection to reason about the equivalence of the ... :>: "sizes" of supposedly infinite sets, ... Two sets have the same cardinality ...
    (sci.math)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... We use the concept of bijection to reason about the equivalence of the ... "sizes" of supposedly infinite sets, ... If we defined "same cardinality" differently then of course ...
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  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... of his arguments for Zenkin, in case your formalization is correct, ... We use the concept of bijection to reason about the equivalence of the ... "sizes" of supposedly infinite sets, ...
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  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... of his arguments for Zenkin, in case your formalization is correct, ... We use the concept of bijection to reason about the equivalence of the ... "sizes" of supposedly infinite sets, ...
    (comp.theory)
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