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Topic: Why does Cantor's diagonal argument fail?
Replies: 3   Last Post: Jan 18, 2014 7:24 PM

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Ben Bacarisse

Posts: 994
Registered: 7/4/07
Re: Why does Cantor's diagonal argument fail?
Posted: Jan 18, 2014 2:25 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Saturday, 18 January 2014 14:53:43 UTC+1, Ben Bacarisse wrote:
>> mueckenh@rz.fh-augsburg.de writes:
>>
>> <snip>
>>

>> > Of course. I have been quoting an exceptionally simple example for years:
>> >
>> > 0.0
>> > 0.1
>> > 0.11
>> > 0.111
>> > ...
>> >
>> > If the antidiagonal is constructed by the replacement of 0 by 1 then
>> > list and diagonal and antidiagonal are all well defined: The list as
>> > the sequence of finite approximations of 1/9, the diagonal as zero,
>> > and the antidiagonal as 1/9.

>>
>> ...which differs from all entries.

>
> Of course, but


Ha! Does it differ from all entries or not? Is this a question that
can be answered in WMaths? Can two numbers differ and not differ in
WMaths?

<snip>

--
Ben.



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