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In article <UeiTg.25580$QT.16960@xxxxxxxxxxxxxxxxxxxxx>,
Poker Joker <Poker@xxxxxxxxx> wrote:
>
>"Arturo Magidin" <magidin@xxxxxxxxxxxxxxxxx> wrote in message
>news:efj3bk$120f$1@xxxxxxxxxxxxxxxxxxxxx
>> In article <N_YSg.1208$3E2.403@xxxxxxxxxxxxxxxxxxxxx>,
>> Poker Joker <Poker@xxxxxxxxx> wrote:
>>>
>>>"Arturo Magidin" <magidin@xxxxxxxxxxxxxxxxx> wrote in message
>>>news:efgfhd$261u$1@xxxxxxxxxxxxxxxxxxxxx
>>>> In article <1159410937.013643.192240@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>>>> <the_wign@xxxxxxxxx> wrote:
>>>>>Cantor's proof is one of the most popular topics on this NG. It
>>>>>seems that people are confused or uncomfortable with it, so
>>>>>I've tried to summarize it to the simplest terms:
>>>>>
>>>>>1. Assume there is a list containing all the reals.
>>>>>2. Show that a real can be defined/constructed from that list.
>>>>>3. Show why the real from step 2 is not on the list.
>>>>>4. Conclude that the premise is wrong because of the contradiction.
>>>>
>>>> This is hardly the simplest terms. Much simpler is to do a ->direct<-
>>>> proof instead of a proof by contradiction.
>>>>
>>>> 1. Take ANY list of real numbers.
>>>> 2. Show that a real can be defined/constructed from that list.
>>>> 3. Show that the real from step 2 is not on the list.
>>>> 4. Conclude that no list can contain all reals.
>>>>
>>>
>>>How can it be simpler if the list can be ANY list instead of a
>>>particular one.
>>
>> Because a direct proof is simpler than a proof by contradiction.
>>
>>> ANY list opens up more possiblities than
>>>a single list.
>>
>> Any list does not require you to assume that there is a "single list"
>> which some some particular property.
>
>We all noticed you neglected this logic:
Hardly.
>if its true for ANY list, then it must be
>true for a specific list.
Indeed.
>So if considering a single specific list
>shows a flaw, then looking at ANY (ALL of them) list doesn't
>help.
And if my grandmother had wheels, then she'd be a bicycle. Since she
doesn't, a discussion about just what kind of bicycle she might be in
that case is a waste of time.
Likewise, since no flaw has been exhibited by looking at any specific
list (and "specific" in this case must mean explicit and specific, not
a putative list with putative properties whose existence cannot be
established a priori; otherwise, we might just say "take a list for
which the argument does not work", which is of course nonsense),
discussions about this are a waste of time.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
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